This paper investigates the predefined-time adaptive distributed optimal control problem for nonlinear multiagent systems with unknown dynamics and actuator saturation. A novel predefined-time distributed optimal controller is formulated by using neural network and differential graphical game. To solve the predefined-time optimal control design problem, a neural network reinforcement learning algorithm is developed to learn the solutions of the optimal controller and Hamilton-Jacobi-Bellman equation, where the updating laws of the critic network weights are designed via current and historical data. It is proved the controlled nonlinear multiagent systems are predefined-time stable and achieve the Nash equilibrium within a finite settling time. Finally the computer simulation results illustrate the effectiveness of the proposed distributed optimal control scheme.

This paper investigates the adaptive fuzzy predefined-time distributed time-varying optimal consensus control problem for high-order nonlinear multi-agent (NMA) systems under unbalanced graphs. Under the predefined-time stability theory, a distributed predefined-time estimator in an unbalanced network is designed to obtain distributed optimal reference signal. Since the higher-order derivatives of the obtained distributed optimal reference signal do not exist, a command filter is designed to avoid computing them. Based on the designed predefined-time estimator and command filter, a predefined-time adaptive fuzzy consensus tracking control scheme is proposed by using backstepping control technology. It is proven that the controlled NMA system is predefined-time stable, and the agents’ outputs converge to the optimal trajectory within a predefined time. Finally, we apply the adaptive fuzzy predefined-time distributed time-varying optimal consensus control method to marine surface vehicles, and the simulation results confirm its effectiveness.

This paper investigates the fuzzy distributed resilient formation control problem of Takagi–Sugeno (T–S) fuzzy MASs under DoS attacks and communication delays. Since the communication network among MASs is subject to DoS attacks and communication delays, the leader’s states cannot be obtained continuously by each agent. A fuzzy distributed resilient estimator is first proposed to estimate the leader’s state subject to DoS attacks and communication delays. By constructing a Lyapunov-Krasovskii functional, it is demonstrated that the estimation errors of the fuzzy resilient estimator exponentially converge to zero. Secondly, based on the formulated fuzzy distributed resilient estimator and parallel distributed compensation (PDC) algorithm, a fuzzy distributed resilient formation controller is developed. The presented fuzzy distributed resilient formation control strategy ensures that the controlled T–S fuzzy MASs remain stable and achieve the formation objective. Finally, the developed fuzzy distributed resilient formation control method is applied to the single-link robot arm systems, the effectiveness is demonstrated by simulation and comparison results.

This article studies the distributed observer-based event-triggered (ET) optimal control problem for nonlinear multiagent systems (NMASs) over jointly connected digraphs. Since agents cannot get the leader under jointly connected digraphs, a distributed observer is constructed to estimate the unknown leader. At the same time, to enhance the efficiency of communication resources utilization between agents, an ET communication mechanism is developed to schedule the agent communication. Subsequently, neural networks (NNs) are adopted to handle the unknown nonlinearities, and an NN state observer is established to reconstruct the unmeasurable states. By utilizing the backstepping technique and adaptive dynamic programming theory, a distributed observer-based ET optimal control algorithm is developed, in which a critic network is designed with a proposed weight updating law to estimate the cost function. It is proven that the presented ET optimal control approach ensures that all signals of NMASs are uniformly ultimately bounded (UUB), and the cost function is minimized. At last, the theoretical results are applied to marine surface vehicles (MSVs) to validate the efficiency of the developed optimal control strategy.

This paper investigates the distributed adaptive event-triggered least-distance formation control problem for nonlinear multiagent systems (MASs) over switching digraphs via noncooperative game theory. First, distributed event-triggered estimators incorporating a switching-activated communication strategy are proposed to estimate the moving target and all agents’ decisions while reducing inter-agent communication. Based on the designed distributed estimators, a distributed time-varying Nash equilibrium (NE) seeking algorithm is established such that all agents’ decisions asymptotically reach the NE solution. Since high-order derivatives of the proposed distributed estimator states do not exist due to digraphs switching and event-triggering, the backstepping control design cannot be implemented. To overcome this difficulty, three-stage cascade filters are designed to provide sufficiently smooth signals. Then, based on the developed three-stage cascade filters, an adaptive event-triggered least-distance formation controller is proposed by the backstepping control technique. It is proved that the constructed formation control method can ensure that all agents achieve the least-distance formation, i.e., all agents’ outputs asymptotically reach a desired shape while minimizing the overall distance to the moving target. Finally, a simulation example on nonholonomic mobile robots is provided to illustrate the validity of the developed theoretical results.

In the cruising mission of the unmanned surface vessel-unmanned aerial vehicle (USV-UAV) cooperative plant, although the UAV is capable of executing aerial maneuvers, it still faces inevitable obstacle avoidance and control challenges in narrow waterways and cross-bridge scenarios. As such, this study proposes a variable-speed multi-port segmented threshold event-triggered cooperative collision avoidance control algorithm based on the geometric velocity obstacle method (GVO). In the guidance module, first define the obstacle zone based on the detected bridge dimensions. Then, by setting safety thresholds and target points, implement a bridge collision avoidance guidance function with an automatic selection mechanism for the narrow waterway navigation mission. In the control module, in the presence of bridge obstacles, a variable-speed multi-port segmented threshold event triggering mechanism (MSETM) is designed for path tracking and collision avoidance missions to ensure the coordination of the USV-UAV cooperative plant at the beginning and end of collision avoidance. Furthermore, a multi-layer neural networks (MNNs) is adopted to approximate the system’s nonlinearities, achieving high approximation accuracy and computational efficiency. Stability of the algorithm is proven using Lyapunov stability theory, and its effectiveness is validated through simulation experiments.

This paper investigates the adaptive fuzzy distributed optimal control problem for nonlinear multiagent systems (MASs) under the predefined-time stability theory. The addressed controlled nonlinear MASs contain unknown dynamics, immeasurable states, and input saturations. To solve unknown dynamics and immeasurable states problems, fuzzy logic systems (FLSs) are used to model the uncertain nonlinear MASs, and an adaptive fuzzy distributed state observer is designed to estimate the unknown states. Then, based on the designed state observer and differential graphical game, a predefined-time distributed optimal output feedback controller is formulated. To implement the fuzzy distributed optimal output feedback controller, a fuzzy reinforcement learning algorithm is proposed to learn the solution of the Hamilton-Jacobi-Bellman (HJB) equation, in which fuzzy logic systems are used as a critical network, and its weights adaptive laws are designed by current and historical data. It is proven that the proposed adaptive fuzzy distributed optimal controller with reinforcement learning algorithm can guarantee the closed-loop system is asymptotically stable and reaches the Nash equilibrium within the given finite-time settling time without needing the restrictive persistent excitation (PE) condition. Finally, the computer simulation results and comparison with the existing optimal control method illustrate the effectiveness of the proposed distributed optimal control scheme.

This paper presents a fuzzy event-driven optimal quantized feedback control strategy for unmanned surface vehicle (USV) trajectory tracking under multiple practical constraints, including limited maritime communication resources, model uncertainties, thruster saturation, and positioning constraints. To address the communication limitation, a signal quantization and event-driven mechanism is introduced, where the thruster quantization is characterized by a linear analytical model. A fuzzy adaptive observer (FAO) is used to estimate the quantized feedback signal, while a finite-time disturbance observer (FDO) estimates environmental disturbances. Additionally, a dynamic auxiliary system compensates for thruster saturation effects. A logarithmic barrier function-based constraint mechanism ensures positioning variables remain within predefined safety bounds. The adaptive quantized feedback controller is designed using the backstepping framework and dynamic surface control techniques, with an optimal compensation term based on adaptive dynamic programming (ADP) to minimize the cost function of the tracking error system. The proposed control strategy ensures that all closed-loop signals remain within specified limits. Simulation results confirm the effectiveness and advantages of this approach.

In this article, we study the reinforcement learning (RL) optimal output feedback control problem for Takagi–Sugeno (T–S) fuzzy systems with immeasurable states and disturbances. A fuzzy filtering observer is designed to estimate the immeasurable states, and then, based on the filtering observer, a fuzzy optimal output feedback control method is presented by employing zero-sum differential game theory. Since the analytical optimal control solutions are reduced to solving game algebraic Riccati equations (GAREs), which is difficult to obtain their analytical solutions, an output feedback model-free policy iteration (PI) learning algorithm is proposed. It is proved that the proposed algorithm is convergent and the proposed fuzzy RL optimal output feedback control approach can make the controlled systems be asymptotically stable and satisfy the disturbance attenuation condition. Finally, we apply the developed optimal control method to a mass–spring–damper system, and the simulation results verify the effectiveness of the developed method.

This article studies the game-based fuzzy adaptive least-distance formation control problem for nonlinear multiagent systems (MASs) under event-triggered communication. Since agents cannot obtain the nonneighboring agents’ actions, and a subset of agents cannot access the moving target, distributed event-triggered observers are designed to estimate all agents’ actions and the moving target. Based on the designed distributed observers, a distributed time-varying Nash equilibrium (NE) seeking strategy is constructed such that the agents’ actions asymptotically converge to the NE. To overcome the nonexistence problem of high-order derivatives of the estimated signals arising from intermittent communication, three stage cascade filters are proposed to generate sufficiently smooth signals to replace the estimated signals. Then, a fuzzy least-distance formation controller is developed by utilizing the proposed cascade filters and the backstepping control theory. It is proven that the proposed formation control scheme can guarantee that all agents asymptotically achieve the least-distance formation. Finally, simulation and comparison results on marine surface vehicles (MSVs) verify the effectiveness of the proposed control scheme.

This article investigates the adaptive neural network (NN) cooperative optimal output-feedback control problem for nonlinear multi-agent (NMA) systems under switching topology. Since the optimization point of global cost function is unknown, an optimal signal generator and high-order filter are established to estimate optimization point and high-order derivatives of optimal virtual signals. Meanwhile, a NN state observer is designed to estimate unmeasurable states. Based on the NN state observer and high-order filter, an adaptive NN cooperative optimal output-feedback control scheme is proposed by backstepping control design technology. It is shown that the proposed adaptive NN cooperative optimal output-feedback control method ensures that all signals of systems are bounded and the global cost function is minimized. In addition, we apply the proposed cooperative optimal control approach to unmanned surface vehicle systems, the simulation results verify its effectiveness.

This paper addresses the challenge of adaptive fuzzy event-triggered bipartite consensus control for a class of nonlinear multi-agent systems (MASs) with full-state asymmetric constraints, incorporating both cooperative and adversarial communication between agents. To ensure consensus tracking performance in the presence of asymmetric full-state constraints, the nonlinear MASs are augmented with an enhanced nonlinear function. Fuzzy logic systems (FLSs) are employed to handle unfamiliar nonlinearities effectively. To reduce the communication burden and enhance transient performance, an event-triggered control strategy is introduced, accompanied by the construction of an observer utilizing triggered output signals to assess unmeasured states. Furthermore, the control scheme is formulated by integrating dynamic surface control (DSC) and adaptive backstepping techniques. The validity of the proposed approach is verified through Lyapunov’s theory, demonstrating that all signals within the closed-loop system are bounded. Simulation results further support the effectiveness of the proposed methodology.Note to Practitioners—With the rapid development and deep integration of intelligent control theory, the control design of MASs is still challenging in many engineering problems. However, in practical applications, there is not only cooperation but also competition between agents, and the system states are unmeasured and subject to various forms of constraints. To solve this problem, we introduce an improved nonlinear transformation function. When network resources are limited, continuous communication is sometimes not feasible in engineering applications. To minimize the communication burden, we propose an event-triggered control strategy, which combines dynamic surface control technology and adaptive backstepping technology to design the trigger controller. The proposed scheme can effectively save resources and deal with various constraints of system states and may be applied to other similar engineering fields.

This paper is concerned with the distributed optimal consensus problem of multi-agent systems with uncertain nonlinear dynamics. The essential work of this paper is the development of an exact-optimal consensus control methodology via fuzzy adaptive control technique. Specially, an optimal signal generator for each agent is established to cooperatively estimate the accurately global optimal solution. Subsequently, a novel fuzzy adaptive controller is designed with the aid of command filtered backstepping and adaptive compensation technique, making it powerful enough to the fuzzy approximate error and filtering error. Thereby, it provides a concise optimal consensus control algorithm for strict-feedback nonlinear systems, which avoids the requirement that the gradient of the local cost function is high-order differentiable. Based on Lyapunov stability theory, it is proven that the outputs of all agents synchronize to an optimal agreement with asymptotic convergence; i.e., the exact-optimal consensus is able to be guaranteed under the proposed control approach. Finally, simulation studies and comparisons are presented to show the effectiveness of the proposed control approach.Note to Practitioners—This paper addresses the distributed optimal consensus problem of nonlinear multi-agent systems with uncertain dynamics, which is more challengeable. It is the first effort to study the exact-optimal consensus control problem via function approximation technique. Through constructing multiple optimal signal generators to cooperatively estimate the accurately global optimal solution, the distributed optimal consensus control is converted into an asymptotic tracking control. Then, a concise optimal consensus control is proposed by command filtered backstepping technique, which is easy to implement in practice. The developed control protocol can be applied to unmaned swarm systems, and it has contributions to academic and practical applications.

In this study, the adaptive fuzzy collision-free formation control issue is investigated for uncertain nonlinear multiagent systems (MASs) under communication delays. Fuzzy logic systems (FLSs) are applied to model unknown agents, and the navigation function is utilized to establish the criterions of collision avoidance and connectivity preservation for the agents. Since the communication between agents is affected by time-varying delays, the leader's state and its high-order derivatives' real-time information are unknown, a distributed command governor is designed to estimate them. Based on the designed distributed command governor, and the collision avoidance and connectivity preservation criterions, an adaptive fuzzy collision-free formation control approach is formulated by backstepping control design theory. The developed adaptive fuzzy formation control approach can not only achieve the formation objective, but also avoid the collisions and ensure the topology connectivity. Finally, we apply the developed adaptive fuzzy formation control method to multiple Euler-Lagrangian (EL) systems, the simulation and comparison results verify its effectiveness.

This article investigates the adaptive fuzzy distributed optimal event-triggered (ET) control problem for high-order nonlinear multiagent (NMA) system under weight-unbalanced directed graph. An optimal signal generator with ET mechanism is first established to estimate optimization point and optimal network channel utilization between agents and neighbors. Second, since the ET mechanism is introduced in optimal signal generator, the first-order derivative of optimal virtual signals is not continuous at the trigger instant, a high-order filter is established to estimate high-order derivatives of optimal virtual signals. Based on the optimal signal generator with ET mechanism and high-order filter, an adaptive fuzzy distributed optimal ET control scheme is proposed by backstepping control design technology. It is shown that controlled NMA system is asymptotically stable and the global cost function is minimized. Finally, we apply the proposed distributed optimal ET control approach to marine surface vehicle systems, the simulation and comparison results verify its effectiveness.

This article focuses on the prescribed-time fully distributed Nash equilibrium seeking (PT-FDNES) against denial-of-service attacks of multiagent systems (MASs), where the action of each agent is described by high-order uncertain nonlinear dynamics. Specifically, the fuzzy logic system technique is utilized to approximate the unknown nonlinear functions existing in the agents' dynamics, where a single parameter updating law is proposed by estimating the norm of fuzzy optimal weight vectors to further reduce the computational cost. To deal with the difficulty where the attack-induced topologies may destabilize the NE seeking performance, a novel PT function together with a resetting mechanism is delicately designed. Then, a PT-FDNES with adaptive gains is developed by incorporating the resetting mechanism to search for the NE independent of any global information. Subsequently, a novel PT fuzzy adaptive tracking control law is designed in the celebrated backstepping structure. Based on the Lyapunov stability theory, we prove that actions of the MAS converge to the NE within the PT and all the closed-loop system signals remain bounded. At last, an example is given to illustrate the effectiveness of the proposed algorithm.

Inverse reinforcement learning optimal control is under the framework of learner-expert, the learner system can learn expert system's trajectory and optimal control policy via a reinforcement learning algorithm and does not need the predefined cost function, so it can solve optimal control problem effectively. This paper develops a fuzzy inverse reinforcement learning optimal control scheme with inverse reinforcement learning algorithm for Takagi-Sugeno (T-S) fuzzy systems with disturbances. Since the controlled fuzzy systems (learner systems) desire to learn or imitate expert system's behavior trajectories, a learner-expert structure is established, where the learner only know the expert system's optimal control policy. To reconstruct expert system's cost function, we develop a model-free inverse Q-learning algorithm that consists of two learning stages: an inner Q-learning iteration loop and an outer inverse optimal iteration loop. The inner loop aims to find fuzzy optimal control policy and the worst-case disturbance input via learner system's cost function by employing zero-sum differential game theory. The outer one is to update learner system's state-penalty weight via only observing expert systems' optimal control policy. The model-free algorithm does not require that the controlled system dynamics are known. It is proved that the designed algorithm is convergent and also the developed inverse reinforcement learning optimal control policy can ensure T-S fuzzy learner system to obtain Nash equilibrium solution. Finally, we apply the presented fuzzy inverse Q-learning optimal control method to nonlinear unmanned surface vehicle system and the computer simulation results verified the effectiveness of the developed scheme.

This article proposes an adaptive fuzzy distributed output-feedback optimal fault tolerant control (FTC) methodology for strict-feedback nonlinear multiagent systems with intermittent actuator faults. The proposed adaptive distributed FTC method is composed of a fuzzy feedforward output-feedback distributed FTC and a fuzzy error feedback distributed optimal controller. The fuzzy feedforward distributed FTC is designed by backstepping design technique and fuzzy state observer, which can solve unmeasured states problem of the agents and transform the strict-feedback nonlinear multiagent systems (MASs) into a linearizable feedback nonlinear MASs. The fuzzy distributed optimal controller is designed for the error nonlinear MASs based on adaptive dynamical programming to find a Nash equilibrium solution of the mutiplayer differential graphical game. It is proved that the formulated adaptive distributed fuzzy optimal FTC scheme can achieve the global optimal control objective, and make the controlled MASs asymptotic stable, the followers' outputs follow the leader's output. The simulation results on ship autopilot systems demonstrate its effectiveness.

This paper investigates the distributed fuzzy adaptive Nash equilibrium (NE) seeking problem in noncooperative games for nonlinear multi-agent systems under unreliable communication networks. Since the considered unreliable communication networks are jointly strongly connected switching networks and suffer from time-delays, agents cannot receive their neighboring agents' actions or can only obtain delayed actions. To estimate the neighboring agents' actions, a distributed NE seeking observer is developed. Then, based on the proposed distributed NE seeking observer and backstepping control technology, a distributed fuzzy adaptive control scheme is constructed by utilizing fuzzy logic systems and adopting integrable functions and bounded parameter estimation algorithms. It is proven that the observation error of the distributed NE seeking observer asymptotically converges to zero, and the developed fuzzy adaptive control scheme can ensure that the agents' outputs asymptotically converge to the NE of the noncooperative game. Moreover, the non-differentiable problem of virtual controllers is avoided. Finally, we apply the distributed fuzzy adaptive control scheme to marine surface vehicles, and the simulation and comparison results confirm its effectiveness.

In this article, we study the distributed fuzzy formation control problem for a class of strict-feedback nonlinear multiagent systems (NMASs) under communication delays and jointly connected switching topology. Since the communication between agents is affected by time-varying delay and some agents cannot access the leader's information under jointly connected switching topology, a communication-delay-related distributed formation observer is designed to estimate the leader's information and simultaneously mitigate the effects of communication delays. By using fuzzy logic systems to approximate the unknown functions, the controlled uncertain NMASs are transformed into the strict-feedback parameterized NMASs. Then, based on the designed communication-delay-related distributed formation observer and the backstepping control design theory, a fuzzy adaptive formation control algorithm is proposed. By constructing the Lyapunov functions, it is proved that the designed communication-delay-related distributed formation observer errors converge to zero exponentially and the proposed distributed fuzzy formation control algorithm can ensure that the closed-loop systems are semi-globally uniformly ultimately bounded, with the formation tracking errors converging to an adjustable neighborhood around zero. Finally, we apply the distributed fuzzy formation control scheme to marine surface vehicles (MSV), the simulation results and comparisons with the previous control methods verify its effectiveness.

This article delves into the adaptive event-triggered control approach for a fleet of underactuated unmanned surface vehicles (USVs) that are interconnected through shared switching topologies. The methodology put forth addresses the asynchronous control challenge within this networked framework. By incorporating an event-triggered mechanism, we have crafted the distributed asynchronous observers to approximate the reference signal, capitalizing on the dynamics of distributed errors. Leveraging fuzzy logical systems, we have devised control inputs for the underactuated USVs by employing the backstepping technique. Utilizing Lyapunov stability theory, we have rigorously demonstrated that these control inputs facilitate tracking of the reference signal by the USVs, contingent upon their relative positions. This article concludes with a validation of the proposed control strategy, showcasing its effectiveness in practical scenarios.

The adaptive neural network (NN) exact-optimal consensus fault tolerant control (FTC) problem is investigated for uncertain high-order nonlinear multiagent systems (NMASs) with intermittent actuator faults. NNs are utilized to model unknown agents, and an adaptive NN state observer with asymptotical property is established. Since the optimization point is not directly known to the agents, the optimal signal generator is formulated to estimate it. Based on the designed NN state observer and optimal signal generator, an adaptive NN exact-optimal consensus output-feedback FTC scheme is proposed by using the backstepping control technology. It is proved that the controlled NMAS is asymptotically stable, and the observer errors and the tracking errors between the outputs and optimization point asymptotically converge to zero. Finally, we apply the proposed adaptive NN exact-optimal consensus output-feedback FTC approach to multiple marine surface vehicles (MSVs), and the simulation and comparison results verify its effectiveness.

This article focuses on addressing adaptive fixed-time optimal control problem for state-constrained nonlinear systems with uncertain dynamics. First, new barrier optimal cost functions are constructed for subsystems to achieve optimal control performance. To achieve this, actor-critic structures are proposed to acquire the optimal fixed-time controller, utilizing universal approximator (e.g., neural networks) to estimate unknown system nonlinearities. Then, a method ensuring tracking error to converge to a prescribed region is formulated under certain bound condition (i.e., full-state constraints are not violated). The implementation of this method is through integrating prescribed exponential function into barrier Lyapunov functions. Moreover, it is worth noting that the proposed optimal control scheme can guarantee that all closed-loop signals are bounded in fixed time and that the convergence precision of tracking error can be prescribed a priori. Finally, one numerical example is provided to show the effectiveness of the proposed optimal fixed-time control approach.

In this article, the problem of adaptive event-triggered tracking control is investigated for a class of nonlinear multiagent systems (MASs) with asymmetric multi-information-related (MIR) constraints on all states. The fuzzy-logic systems (FLSs) are utilized to model the system unknown items by virtue of their universal approximation properties. The appropriate integral barrier Lyapunov functions (IBLFs) are selected to prevent the states from exceeding the asymmetric constraint boundaries associated with multi-information, which include historical states, time and neighbor outputs. The event-triggered mechanism (ETM) with varying threshold is employed to reduce the update frequency of the controller, thereby achieving the purpose of saving network resources, including communication bandwidth and computation abilities. Under the backstepping technique framework, the required control scheme is designed by integrating the adaptive controller with triggering mechanism. And it is proven that the controlled plant with state constraint conditions is stable, the consensus tracking errors can eventually remain near the origin, and the Zeno behavior does not exist. Finally, the simulation results corroborate the view that the designed control scheme is effective.

An adaptive fuzzy command filtering backstepping technique is given for strict-feedback fractional-order uncertain nonlinear systems. The controlled system includes unknown nonlinear functions, as well as state and input quantization. Considering fractional-order nonlinear systems that do not satisfy matching conditions, unknown nonlinear functions are approximated by fuzzy logic systems, and a sector bounded quantizer is used to quantify all input and state variables. During the plan process, command filtering backstepping scheme is used to avoid the use of nonsmooth states. Subsequently, in order to ensure the boundedness of a series of errors caused by continuous original states for stability analysis and discontinuous quantization states for control, a sufficiently smooth fractional-order projection operator is proposed. In addition, the fractional-order uniformly bounded criterion has been established and strictly proven, which solves the problem of uniformly bounded error signals in the fractional-order sense under the premise of known parameter boundedness. Thus, the boundedness of all closed-loop signals is ensured by the fractional-order uniformly bounded criterion. Finally, the simulation results have confirmed the efficacy of the method.

This article focuses on the trajectory tracking control of under-actuated unmanned surface vehicles subject to unknown ocean current and input quantization. Regarding kinematics, we devise an extended-state-observer-based guidance law capable of compensating for ocean currents to track the intended trajectory. Concerning kinetics, we propose an event-triggered adaptive fuzzy quantization control law using a linear analytical model to depict input quantization, eliminating the need for prior quantization parameter information. A notable aspect is the reduction in both execution frequency and magnitude, thereby mitigating communication burdens. The stability of this control strategy is proofed through input-to-state stability analysis. Simulation experiments are conducted to affirm the viability of the event-triggered adaptive fuzzy quantization control strategy.

In this article, a fuzzy optimal event-triggered dynamic positioning control approach with aQ-learning value iteration (VI) algorithm is developed for unmanned surface vehicles (USVs) systems. The USV systems are first modeled by Takagi-Sugeno (T-S) fuzzy systems. To reduce the communication resources and controller update times, an event-triggered mechanism is designed via employing the sampled augmented systems states and triggered control input signals. Based on the developed event-triggered mechanism and Bellman optimality theory, a fuzzy optimal event-triggered control (ETC) approach is presented. Since solution of optimal control policy reduces to algebraic Riccati equations (AREs), its analytical solution is difficult to solve directly. Then, to search its approximation solution, a VI algorithm is formulated. By rigorous proof, the proposed optimal ETC scheme can assure that the USVs systems are asymptotically stable and theQ-learning algorithm is convergent. Finally, the simulation and comparisons results with previous optimal controllers verify the feasibility of the presented optimal ETC scheme.

This article proposes a new adaptive fuzzy distributed output-feedback optimal control methodology for high-order strict-feedback nonlinear multiagent systems (MASs), which is composed of a fuzzy feedforward output-feedback distributed controller and a fuzzy error feedback correction distributed optimal controller. The fuzzy feedforward distributed controller is designed by backstepping design technique and fuzzy state observer, which can solve unmeasured states problem of the agents and transform the high-order strict-feedback nonlinear MASs into a linearizable feedback nonlinear MASs, while the fuzzy error feedback correction distributed controller is designed for the error nonlinear MASs based on adaptive dynamic programming and multiplayer differential graphical game, which can find a Nash equilibrium solution of the muti-player differential graphical game. It is proved that the formulated adaptive distributed fuzzy optimal control scheme can achieve the global optimal control objective, and make the controlled MASs stable, the followers output follow the leaders output. The simulation results on ship autopilot systems demonstrate its effectiveness.

In this article, the collision-free adaptive fuzzy secure formation control problem is investigated for uncertain nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks. Since the DoS attacks block the signal transmission between agents, the leader’s states and output are inaccessible to the followers, a distributed command governor is designed to estimate them. To avoid the collisions among the agents or between the agents and the dynamics obstacles, the integral-type barrier Lyapunov function (BLF) is employed to develop a secure collision-free adaptive fuzzy formation controller based on the designed governor. It is shown that the developed secure collision-free formation control approach can not only achieve the formation objective, but also avoid the collisions under DoS attacks. Finally, we apply the developed secure collision free formation control method to multiple Euler–Lagrangian (EL) systems, the simulation and comparison results verify its effectiveness.

This paper presents a nonlinear filters-based adaptive fuzzy control design for strict-feedback nonlinear systems with unknown asymmetric dead-zone output and virtual control coefficients. First, a novel smooth approximation of the non-smooth asymmetric output dead-zone nonlinearity is constructed to improve the approximation performance and speed. Then, to dilute the effects of unknown dead-zone and virtual control coefficients, an adaptive compensation mechanism is presented by utilizing projection operators techniques and the properties of fuzzy basis functions and hyperbolic tangent functions. Further, a novel adaptive backstepping control design method based on the nonlinear filters is proposed, which not only avoids the issue of explosion of complexity inherent in the backstepping procedure, but also completely compensates the effects of the boundary errors generated by the introduced filters in spite of unknown virtual control coefficients. From the properties of the smooth projection operator, and based on Lyapunov synthesis, it is shown that all closed-loop signals are ensured uniformly bounded. Finally, the applicability of the proposed control method is rigorously verified by a example of one-link manipulator with a brushed dc motor.Note to Practitioners—Strict-feedback nonlinear systems can be utilized to model many practical engineering systems, such as one-link manipulator, permanent magnet synchronous motor, robots with flexible joints, spacecrafts, etc. Due to the physical limitations and other factors, non-smooth dead-zone nonlinearity often presents in system components, which will influence the control performance and threat the operation security. Therefore, this paper considers the control design problem for strict-feedback nonlinear systems with unknown asymmetric dead-zone output nonlinearity, and the proposed control algorithm is successfully applied to one-link manipulator with a brushed dc motor. In addition, the virtual control coefficients are often assumed to be known constants or known nonlinear functions with known bounds in the existing results, which is unrealistic on account of the economic costs and environmental factors. To erase such limitation, this paper presents a novel adaptive compensation mechanism based on smooth auxiliary function dependent on the property of tanh-function and the projection operator technique.

This paper investigates adaptive neural network filtering control for uncertain nonlinear systems with general model state and input quantization. The plants under consideration contain quantized states, quantized input, and unknown nonlinear system functions. A universal quantizer is established for both system states and control input. In the control design process, neural networks and the command filter are used to approximate the unknown nonlinear system functions and overcome the discontinuities of virtual control signals, respectively. A new command filtering-based control strategy is proposed using the backstepping design technique. It is testified that the proposed control approach can guarantee that the closed-loop signals are semi-global uniform ultimate boundedness. A simulation example is presented to further demonstrate our proposed scheme’s effectiveness.Note to Practitioners—This work is motivated by the quantized control problem for a class of nonlinear systems with state and input quantization. In modern control engineering applications, quantization plays a crucial role due to the prevalent use of digital processors that operate with finite precision arithmetic. It is valuable and inevitable to minimize information flow, reduce communication burden, and improve system security. However, quantization will introduce significant discontinuous characteristics and strong nonlinearity, which may decrease the system’s performance and even drive the closed-loop system to instability. This paper demonstrates how to use backstepping and adaptive control methods with command filter to complete controller design and deal with the quantization effects. Therefore, it provides a feasible approach for engineering applications.

This paper considers a prescribed performance-based event-triggered model-free adaptive control (ET-MFAC) problem for nonlinear system without and with false data injection (FDI) attacks. First, the nonlinear system is converted into an equivalent linear data model by utilizing the dynamic linearization technique. Then, the event-triggered constrained tracking control schemes for nonlinear system without and with FDI attacks under the data-driven framework are designed, which include the following three parts: 1) a prescribed performance function and converted output signal are directly employed in the cost function, and the constraint control schemes are derived by the cost function to realize the prescribed performance requirement; 2) an event-triggered mechanism is designed on the basis of the relationship between measurement error and tracking error, which can decrease the communication burden; 3) in order to reduce the negative effect of FDI attacks on nonlinear system, a resilient security control scheme is presented. Finally, a numerical example shows the efficiency of the developed control methods without and with FDI attacks.Note to Practitioners—This paper investigates an event-triggered constrained tracking error control for the nonlinear system without and with FDI attacks. To avoid utilizing accurate model information, MFAC is introduced into the design process of presented strategies. Incorporating prescribed performance control with an event-triggered mechanism, the developed constrained tracking strategy is designed for the first time to lessen the computational burden while improving the transient and steady-state performance on system. Moreover, based on the energy constraint of FDI attackers, a novel resilient security constrained tracking strategy is developed to decrease the impact of FDI attacks on considered nonlinear system. The validity of theoretical results is carried out by a simulation.

In this paper, the near optimal control problem of discrete-time switched nonlinear system with hysteresis is studied, that is, an optimal control scheme is designed for the approximate model of discrete-time switched nonlinear system. Firstly, through system transformation, the original system is replaced with a prediction model that can avoid non causal problems caused by the use of future information in the current step. By using action-critic network, an adaptive control method is put forward to offset the influence of hysteresis. Meanwhile, the designed controller ensures the stability of the closed-loop system under arbitrary switching signal and minimizes the performance index of the subsystem corresponding to the working interval. Finally, the simulation verifies the significance of the proposed method.

This article proposes a stabilization scheme for a cascaded parabolic partial differential equation (PDE)-ordinary differential equation (ODE) system with state constraints. To begin, by employing the fuzzy-logic system (FLS) technique for the unknown nonlinear functions in the ODE subsystem, the influence of the nonlinearities is successfully eliminated. Then, the infinite and finite-dimensional backstepping methods are skillfully applied to the design of control schemes. Specifically, the infinite-dimensional backstepping transformation and its inverse are utilized to obtain a new PDE subsystem, which is convenient for control design. Next, based on the new target PDE-ODE cascade system, a novel first-order filter is subtly introduced into each step of the finite-dimensional backstepping-based controller design procedure to avoid the issue of "explosion of complexity." Furthermore, a novel barrier Lyapunov function (BLF) is constructed to guarantee that the states of the ODE subsystem do not violate the constraints. The controller designed in this article ensures that all signals in the closed-loop system are bounded and the states can converge to zero. Finally, a simulation example verifies that the proposed scheme can achieve satisfactory performance.

This article proposes a novel output-feedback event-triggered control protocol for a class of interconnected parametric nonlinear systems. Different from most existing works where event-triggering mechanisms are considered for only the controller-to-actuator channel or the sensor-to-controller channel, this work adopts event-triggering mechanisms for both channels as well as adaptive laws. An adaptive states observer is designed to estimate the unavailable system state and then a novel adaptive event-triggered controller is proposed based on the celebrated backstepping technique. By utilizing the cyclic small-gain theorem and Lyapunov theory, it is shown that the proposed control scheme ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), and the Zeno behavior is successfully excluded. Finally, a practical example is provided to illustrate the effectiveness and advantages of the proposed approach.

In this article, a fuzzy adaptive fixed-time asymptotic consistent control scheme is developed for a class of nonlinear multiagent systems (NMASs) with a nonstrict-feedback (NSF) structure. In the control process, a fixed-time consistency control method without control singularity is proposed by combining fuzzy logic systems (FLSs) with good approximation capability, fixed-time stability theory, and plus power integration techniques. Then, by using Barbalat's Lemma, the asymptotic stability of tracking errors and the boundedness of the controlled systems are successfully achieved, which means that the tracking errors can converge to zero in a fixed time. Finally, the effectiveness of the designed control scheme is demonstrated by a simulation example.

This article investigates the distributed generalized Nash equilibrium (GNE) seeking problem of noncooperative games (NGs) for high-order strict-feedback nonlinear multiagent systems (MASs). In particular, the feasible action set of each agent is not only subject to local set and inequality constraints but also coupled through an equality constraint with other agents. This constraint structure is more general and covers most of the constraints in the GNE seeking literature. To accomplish the concerned GNE seeking objective, we propose a novel hierarchical GNE seeking approach in this article to decouple the distributed GNE seeking algorithm design into two layers. First, we construct a distributed primary-dual GNE estimator to generate virtual reference signals that converge to the GNE. Then, with the output of the estimator as the reference signal, we develop an adaptive tracking controller to solve the resultant tracking problems under output constraints. To overcome the negative effects of the disturbances, novel compensating terms associated with smooth functions and positive integrable time-varying functions are incorporated in the controller design, which thereby realizes the exact GNE seeking in the presence of nonvanishing mismatched disturbances. At last, an example is given to support the theoretical analysis of the proposed algorithms.

This article studies the fuzzy adaptive event-triggered (ET) consensus control issue of nonlinear multiagent systems (NMASs) under jointly connected switching networks. Since the leader and its high-order derivatives are unknown under jointly connected switching networks, a novel distributed ET reference generator equipped with an ET mechanism is constructed to estimate them. Meanwhile, the continuous information transmission among agents is avoided and the network channel utilization is optimized. Subsequently, fuzzy logic systems (FLSs) are employed to approximate unknown dynamics, and a fuzzy adaptive ET consensus control algorithm only using intermittent communication is designed by backstepping control methodology. It is demonstrated that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), with the tracking errors converging to a small neighborhood around zero. Finally, we apply the developed fuzzy adaptive ET consensus control algorithm to unmanned surface vehicles (USVs), and the simulation results verify the effectiveness of the proposed ET consensus control algorithm.

In this article, the fuzzy adaptive fixed-time bipartite output consistent tracking problem of nonlinear coopetition multi-agent systems (MASs) under a signed directed graph is studied. The fuzzy logic system (FLS) is used in the control scheme to approximate the unknown nonlinear dynamics. Under the framework of adaptive backstepping recursive design, an adaptive fuzzy fixed-time bipartite output consistent control method is proposed. In addition, to further enhance tracking performance, a fixed-time prescribed performance function (FTPPF) is introduced into the control design process, ensuring that the bipartite consensus tracking errors converge within a fixed time to the predefined boundary. By constructing the Lyapunov function, the fixed-time stability of the closed-loop system is proved. Eventually, the feasibility and effectiveness of the proposed adaptive bipartite output consensus control method are verified by the numerical simulation example.

The fuzzy adaptive exact-optimal consensus output-feedback control problem is investigated for uncertain nonlinear high-order multiagent systems (MASs) with unmeasurable states and unknown nonlinear dynamics. Fuzzy logic systems are utilized to model unknown agents; a fuzzy state observer with asymptotical property is established. Since the optimal point is unknown, optimal signal generator is formulated to obtain the optimal point. Based on the designed fuzzy state observer and optimal signal generator, a fuzzy adaptive exact-optimal consensus output-feedback control scheme is proposed by using backstepping control technology. It is proved that the presented control method can guarantee the controlled nonlinear MASs are asymptotically stable and the outputs of all agents asymptotically converge to the optimal point. Finally, we apply the proposed fuzzy adaptive exact-optimal consensus output-feedback control approach to multiple unmanned surface vehicles, the simulation results and comparison results verify its effectiveness.

This paper presents a decentralized adaptive event-triggered fault-tolerant control (FTC) method for switched interconnected nonlinear systems with multiple unpredictable actuator faults, input saturation, and asymmetrical time-varying full-state constraints. Uncertain items and interconnected items are identified by a fuzzy logic system, and a state observer is designed to estimate the unavailable states. By integrating backstepping and command filtering technology, the shortcomings of computational explosion in traditional backstepping are solved. The barrier Lyapunov function (BLF) and the auxiliary system are designed to solve the full-state time-varying constraints and input saturation respectively. By adopting an event-triggered mechanism and estimating the boundaries of unknown fault parameters, an event-triggered FTC controller is designed to achieve the ability of flexibly coordinate control performance and communication burden, and compensate for unpredictable actuator failures. The scheme realizes the situation where arbitrary switching signals and states are unavailable, whether a fault occurs or not, all signals are bounded, and the input and state satisfy the constraints. Finally, the effectiveness of the proposed control method is verified by simulation example.

The distributed optimal problem is investigated in this article for uncertain nonlinear time-varying delay multiagent systems (MASs) under unknown virtual control coefficients. The primary goal is to ensure the output states converge to the ideal point of the global objective function. In comparison to the preceding results on distributed optimization, the considered MASs are subject to time delays and unknown nonlinear functions, which brought great challenges to the controller design process. To overcome this challenge, a distributed optimization algorithm is proposed via a two-stage strategy, which consists of optimization estimator design and tracking controller design. First, in the first-stage, a novel optimal signal generator is constructed by using information interaction between agents, real-time feedback value of local gradient information, so that the optimization problem is transformed into a problem of tracking control. Second, in second-stage, the fuzzy adaptive tracking control strategy is designed via backstepping technology to track the virtual signal accurately. In addition, the Lyapunov–Krasovskii functional (LKF) is applied to counteract influences brought by time-varying delays, and fuzzy logic systems are employed for handling the uncertain function in the derivative of LKF. Furthermore, an assumption is made for the time-varying delays to settle the singularity problem, which often occurs in time-delay problems. In the spirit of the convex analysis and the Barbalats lemma, the stability of the proposed algorithm is illustrated, and all variables in the closed-loop systems are bounded. Lastly, simulations are presented to validate the efficacy of the scheme.

This article studies the integral sliding mode control (ISMC) for fuzzy impulsive stochastic systems with immeasurable states. First, a fuzzy state observer is developed to estimate the immeasurable states. Second, a fuzzy sliding-mode surface and fuzzy ISMC scheme are proposed based on the designed state observer. Then, by constructing a piecewise time-dependent Lyapunov function, the uniformly almost surely exponentially stability of the closed-loop system is proved. Furthermore, a control design algorithm of solving control and observer gains is formulated based on the established sufficient conditions and linear matrix inequality theory. Finally, a simulation example and the simulation comparisons with the existing methods are provided to demonstrate the effectiveness of the proposed fuzzy ISMC scheme.

This article studies the finite-time resilient integral sliding-mode control (ISMC) problem for fuzzy impulsive stochastic systems under denial-of-service (DoS) attacks. A switched state observer is designed to estimate immeasurable states under DoS attacks. Using the designed switched observer and finite-time theory, a fuzzy resilient output feedback ISMC method is proposed. Then, the finite-time stability conditions of the closed-loop system are given. The control design algorithm of solving control and observer gain matrix solutions is formulated by linear matrix inequalities. The effectiveness of the presented control method and analysis is tested by means of a simulation example and comparisons with an existing control approach.

This article considers the finite-time consensus control issue of high-order multi-input and multi-output nonlinear multiagent systems. In the process of establishment, this article uses fuzzy logic systems to identify unknown nonlinear dynamics. Then, according to the backstepping recursive technique and finite-time stability criterion, a fuzzy adaptive finite-time consensus control scheme is designed. At the same time, a communication-restricted control scheme is established according to the dynamic event-triggered strategy with a relative threshold to reduce the execution time of the controller and save communication resources. In addition, a novel integral Lyapunov function is established by introducing the adding power integrator technology, which proves the stability and convergence of consensus tracking errors of closed-loop systems. Finally, taking a marine surface vehicle as an example, the availability of the established event-triggered consensus control scheme is described.

The predefined-time fuzzy adaptive output feedback decentralized fault-tolerant control (FTC) problem is considered for fractional-order nonlinear large-scale systems with intermittent actuator faults. First, the predefined-time stability criterion of fractional-order nonlinear systems is proposed, and then by using fuzzy logic systems to model unknown nonlinear dynamics, a fuzzy decentralized state observer is designed to solve the immeasurable state problem. Second, based on the established predefined-time stability criterion of the fractional-order systems, a predefined-time fuzzy adaptive output feedback decentralized FTC method is developed and the semiglobal practically predefined-time stable of the controlled system is proved. Finally, we apply the developed predefined-time FTC method to fractional-order smooth-air-gap permanent magnet synchronous motor system, the simulation results verify the effectiveness of the proposed predefined-time FTC methodology.

This article addresses the fuzzy adaptive output feedback formation control problem for multiple input and multiple output nonlinear multiagent systems with output saturations and switched topologies. Fuzzy logic systems are employed to model unknown agents, and a state observer is designed to obtain the state information of system. A smooth model is designed to approximate the nonsmooth saturated function by using the continuity of hyperbolic tangent function such that the system outputs can be used for backstepping design. To deal with the nondifferentiable problem of virtual controllers caused by switched topologies, a novel high-order distributed filter is proposed to estimate the local reference signals; then, the continuous local tracking errors instead of the noncontinuous local formation errors are utilized to design the virtual controllers. By utilizing backstepping recursive design, an output feedback formation control scheme is developed. It is proved that the closed-loop signals are all bounded, the leader-follower formation is achieved, and the system outputs are constrained in their saturated bounds. Finally, to show the effectiveness of the developed control method, we apply the developed control method to multiple unmanned surface vehicles).

This article investigates the fuzzy adaptive resilient formation control issue for uncertain nonlinear multiagent systems (MASs) with immeasurable states and under denial-of-service (DoS) attacks. Fuzzy logic systems are utilized to model unknown agents, and a fuzzy state estimator is formulated to reconstruct the agents' unknown states. To obtain the unknown leader information estimation and its high-order derivatives under DoS attacks, a distributed resilient formation estimator is proposed. Based on the designed fuzzy state estimator and resilient formation estimator, a fuzzy output-feedback adaptive resilient formation control scheme is developed via backstepping control methodology. It is proved that the developed fuzzy resilient formation control scheme can guarantee the controlled nonlinear MASs are stable and formation tracking errors converge even under unknown states and DoS attacks. Finally, the proposed fuzzy adaptive resilient formation control method is applied to marine surface vehicles, the simulation results and comparisons show the effectiveness of the presented fuzzy adaptive resilient formation control methodology.

This paper investigates the observer-based fuzzy event-triggered consensus fault-tolerant control (FTC) problem for nonlinear multiagent systems (MASs) with jointly connected switching topologies and actuator faults. Since a part of agents cannot receive information from their neighbors and leader under switching topologies, a distributed observer is designed to estimate unknown leader. At the same time, to avoid continuous information transmission and enhance the efficiency of network resources utilization among agents, an event-triggered communication mechanism is constructed to schedule inter-agent communication. Meanwhile, a fuzzy state observer is formulated to estimate the unmeasured states of the agents. Based on the distributed event-triggered observer and fuzzy state observer, an output-feedback event-triggered fuzzy FTC scheme is proposed by backstepping recursive control design. It is demonstrated that all signals of the controlled MASs are semi-globally uniformly ultimately bounded (SGUUB), consensus tracking errors converge to a small neighborhood of zero, and continuous communication between agents is avoided. Finally, simulation results on marine surface vehicles (MSVs) testify the advantages and effectiveness of the theoretical results.

This article is concerned with the optimized tracking control problem of high-order strict-feedback nonlinear systems with full-state constraints via dynamical event-triggered strategy. An adaptive optimized control algorithm is proposed using the backstepping technique and reinforcement learning method. The algorithm incorporates an identifier–critic–actor architecture and features a flexible design of dynamic event-triggered mechanism (ETM) to decrease signal transmission. The ETM is adaptively adjusted by the estimated fuzzy adaptive weights and design parameters, making it more efficient in terms of communication resources. Moreover, to ensure the system states do not exceed their constrained sets while achieving the optimization objective, a novel performance index function based on the barrier Lyapunov function is constructed. Finally, it can be demonstrated that the system output accurately tracks the desired reference signal, while ensuring that all closed-loop signals remain bounded. Simulation example confirms the validity of the developed design methodology.

This article investigates the fuzzy adaptive output-feedback consensus control problem for nonlinear multiagent systems with network communication encountering deception attacks. Fuzzy logic systems are used to approximate unknown nonlinear functions, and a novel fuzzy state observer is established to estimate the states of encountered deception attacks. For the case of unknown time-varying gains caused by deception attacks, a projection operator-based compensation mechanism is designed. Consequently, under the framework of adaptive backstepping, a novel adaptive fuzzy output-feedback consensus control method is proposed. The proposed control method can not only ensure that all signals remain bounded, but also make all followers maintain consensus with the trajectory of the leader. Finally, the simulation results are given to confirm the effectiveness of the proposed control scheme.

This article addresses a distributed time-varying optimal formation protocol for a class of second-order uncertain nonlinear dynamic multiagent systems (MASs) based on an adaptive neural network (NN) state observer through the backstepping method and simplified reinforcement learning (RL). Each follower agent is subjected to only local information and measurable partial states due to actual sensor limitations. In view of the distributed optimized formation strategic needs, the uncertain nonlinear dynamics and undetectable states may jointly affect the stability of the time-varying cooperative formation control. Furthermore, focusing on Hamilton-Jacobi-Bellman optimization, it is almost incapable of directly dealing with unknown equations. Above uncertainty and immeasurability processed by adaptive state observer and NN simplified RL are further designed to achieve desired second-order formation configuration at the least cost. The optimization protocol can not only solve the undetectable states and realize the prescribed time-varying formation performance on the premise that all the errors are SGUUB, but also prove the stability and update the critics and actors easily. Through the above-mentioned approaches offer an optimal control scheme to address time-varying formation control. Finally, the validity of the theoretical method is proven by the Lyapunov stability theory and digital simulation.

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

This article focuses on the issue of reinforcement learning (RL)-based adaptive optimal finite-time performance constraint control for nonlinear systems. By the aid of RL-based critic-actor neural networks (NNs) construction, an optimal finite-time adaptive performance constraint controller is constructed. Via the adding a power integrator and prescribed performance techniques, a performance constraint-based adaptive finite-time optimal control strategy is developed, which demonstrates the considered system is semi-global practical finite-time stability (SGPFS), and all state errors can remain within a preset error constraint in finite time. Meanwhile, the proposed optimal control strategy can minimum the corresponding cost function. Finally, a numerical example is implemented to verify the feasibility of the developed control strategy and theory.

This article introduces an adaptive fuzzy control methodology employing dynamic event-triggered communication for underactuated multiple unmanned surface vehicles (USVs) with modeling uncertainties. The key innovations of the proposed formation control strategy can be summarized as follows: 1) each USV is equipped with a dynamic event-triggered mechanism, ensuring that the controller and neighboring USVs receive position and yaw angle information only when this mechanism is triggered, enhancing communication efficiency; 2) distributed filters are implemented to continuous the event-triggered information; and 3) by employing the fuzzy logical systems (FLSs) to identify the unknown modeling uncertainties, local observers are designed to estimate unavailable velocity and yaw rate. Based on the dynamic event-triggered mechanism, distributed filters and local observers, a nondifferentiable-free backstepping procedure is proposed. The closed-loop stability is proven through Lyapunov stability theory, and Zeno behavior of the dynamic event-triggered mechanism is demonstrated through reductio. Simulation results are presented to validate the effectiveness of the proposed control strategy.

In this article, the adaptive fuzzy dynamic event-triggered output feedback resilient consensus control issue is investigated for nonlinear multiagent systems (MASs) subject to denial-of-service (DoS) attacks. Fuzzy logic systems (FLSs) are employed to model uncertain agents, and a state observer is constructed to estimate unmeasurable states. An event-triggered distributed resilient observer is designed to save the communication resources between agents, and estimate the unknown leader and its high-order derivatives in case of the communication topology being interrupted by DoS attacks. By the designed state observer and distributed resilient observer, a dynamic event-triggered resilient consensus control method is presented. It is proved that the controlled MASs are stable, and the followers can track the leader under DoS attacks. Moreover, the Zeno behavior can be excluded. Finally, we apply the developed resilient consensus control algorithm to multiple unmanned surface vehicles (USVs), the simulation results verify its effectiveness.

This article studies the fuzzy adaptive event-triggered resilient formation (RF) control problem for nonlinear multiagent systems (MASs) subject to denial-of-service (DoS) attacks and input saturation. Fuzzy logic systems (FLSs) are adopted to identify unknown subsystems, and a fuzzy state estimator is established to address the issue resulted from unmeasurable states. A distributed RF filter is proposed to estimate the unknown leader and obtain the$n$-order derivative of the estimated leader under DoS attacks. To save limited communication resource and reduce the number of controller updates, a switching event-triggered mechanism (SETM) is introduced. Then, a fuzzy event-triggered RF control algorithm is designed via backstepping control method. It is demonstrated that the controlled MASs are stable and formation errors converge even subject to DoS attacks and input saturation. Finally, we apply the event-triggered RF control algorithm to unmanned surface vehicles (USVs), the simulation results verify the effectiveness of the proposed event-triggered RF control algorithm.

This article considers the problem of fixed-time prescribed event-triggered adaptive asymptotic tracking control for nonlinear pure-feedback systems with uncertain disturbances. The fuzzy-logic system (FLS) is introduced to deal with the unknown nonlinear functions in the system. By constructing a new type of Lyapunov function, the restrictive requirement that the upper bounds of the partial derivative of the unknown system functions need to be known is relaxed during the controller design process. At the same time, by developing a novel fixed-time performance function (FPF), the fixed-time prescribed performance (FPP) can be achieved, that is, the tracking error can converge to the neighborhood of the origin in a fixed time and finally converges to zero asymptotically. In addition, the event-triggered strategy is developed to reduce the waste of communication resources. The proposed control law can ensure that all the signals of the system are bounded. Meanwhile, the Zeno behavior can be effectively avoided. Finally, an example is provided to prove the effectiveness of the proposed scheme.

This article addresses the issue of the fuzzy adaptive prescribed performance control (PPC) design for nonstrict feedback multiple input multiple output (MIMO) nonlinear systems in finite time. Unknown nonlinear functions are handled via fuzzy-logic systems (FLSs). By combining the adaptive backstepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which can not only avoid the computational complexity issue but also improve the control performance in contrast to the traditional DSC control methods. Furthermore, to make the tracking errors have the prescribed performance in finite time, a new Lyapunov function is constructed by considering the transform error constraint. Based on the designed Lyapunov functions, it is proved that all the signals of the controlled systems are semiglobal practical finite-time stability (SGPFS). Finally, a simulation example is provided to illustrate the feasibility and validity of the put forward control scheme.

In this article, an adaptive fault-tolerant control (FTC) method and a fractional-order dynamic surface control (DSC) algorithm are jointly proposed to deal with the stabilization problem for a class of multiple-input-multiple-output (MIMO) switched fractional-order nonlinear systems with actuator faults and arbitrary switching. In each MIMO subsystem and each switched subsystem, the neural networks (NNs) are utilized to identify the complicated unknown nonlinearities. A fractional filter DSC technology is adopted to conquer the issue of "explosion of complexity," which may occur when some functions are repeatedly derived. The common Lyapunov function method is used to restrain arbitrary switching problems in the system, and the actuator compensation technique is introduced to tackle the failure faults and bias faults in the actuators. By combining the backstepping DSC design technique and fractional-order stability theory, a novel NN adaptive switching FTC algorithm is proposed. Under the operation of the proposed algorithm, the stability and control performance of the fractional-order systems can be guaranteed. Finally, a simulation example of a permanent magnet synchronous motor (PMSM) system reveals the feasibility and effectiveness of the developed scheme.

In this article, an output feedback adaptive fuzzy tracking control method for a class of switched uncertain nonlinear systems with actuator failures and full-state constraints is proposed under an arbitrary switching signal combining the dynamic surface technique. Since the state variables of the system under study are not measurable, a fuzzy observer is constructed to identify the unmeasured states. The actuator failures are considered in the system. To compensate this failure, a fault-tolerant controller is proposed. Moreover, each state needs to be kept within the constraints, so the tangent Barrier Lyapunov function is selected to solve the full-state constraint problem, and the unknown nonlinear function is approximated by fuzzy-logic systems (FLSs). We also proved that all signals in the closed-loop system are bounded. Furthermore, the states can be kept within the predetermined range even if the actuator fails. Finally, a simulation example is given to verify the effectiveness of the proposed control strategy.

This article addresses the distributed adaptive fuzzy consensus fault-tolerant control (FTC) problem for a class of nonstrict-feedback nonlinear multiagent systems (NMASs) with intermittent actuator faults. The NMASs contain unknown nonlinear dynamics, and actuator faults are the type of intermittent faults. Unknown nonlinear functions have been handled based on fuzzy-logic systems (FLSs) approximation, and the distributed virtual controllers together with their parameter adaptive laws are first designed by combining the adaptive backstepping algorithm and the bounded estimation algorithm. To compensate for the intermittent actuator faults, the novel adaptive fuzzy consensus fault-tolerant controllers are then developed by co-designing the last virtual controllers. On the basis of the Lyapunov theory, the stability analysis of the closed-loop system are given, in which the tracking errors converge to zero asymptotically under the directed communication topologies theory. Finally, the proposed FTC scheme is carried on a group of one-link robotic manipulator systems, and its practicability and effectiveness are verified.

This article studies the output-feedback fixed-time fuzzy consensus control problem for nonlinear multiagent systems (MASs) under the directed communication topologies. Since the controlled systems contain the unmeasurable states and unknown dynamics, the unmeasurable states are reconstructed via linear state observers, and fuzzy logic systems are utilized to identify the unknown internal dynamics. By constructing the integral type Lyapunov function, a fixed-time adaptive fuzzy consensus control scheme is developed by introducing the nonlinear filter technique into the backstepping recursive technique adaptive control algorithm. The presented consensus control method can not only guarantee the controlled system is semi-global practical fixed-time stable (SGPFTS), but also avoid the singular problem in existing backstepping recursive control design methods. Finally, an application of unmanned surface vehicles is provided to verify the effectiveness of the presented fixed-time fuzzy consensus control method.

This article investigates the adaptive neural network (NN) event-triggered containment control problem for a class of nonlinear multiagent systems (MASs). Since the considered nonlinear MASs contain unknown nonlinear dynamics, immeasurable states, and quantized input signals, the NNs are adopted to model unknown agents, and an NN state observer is established by using the intermittent output signal. Subsequently, a novel event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels are established. By decomposing quantized input signals into the sum of two bounded nonlinear functions and based on the adaptive backstepping control and first-order filter design theories, an adaptive NN event-triggered output-feedback containment control scheme is formulated. It is proved that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) and the followers are within a convex hull formed by the leaders. Finally, a simulation example is given to validate the effectiveness of the presented NN containment control scheme.

The event-triggered predefined-time output feedback control problem is considered for fractional-order nonlinear systems (FONSs) with input saturation. The controlled plant contains unknown nonlinear dynamics and unmeasured states. The unknown nonlinear dynamics are handled by using fuzzy approximation technique; a fuzzy state observer is established to estimate unmeasured states and an event-triggered mechanism is given to improve the efficiency of communication resource utilization. The predefined-time stable criterion of FONSs is first developed. Then, an event-triggered predefined-time output feedback control is proposed by using the dynamic surface control technique. Based on the proposed predefined-time stable criterion and Lyapunov function, it is proved that the controlled system is semiglobal practically predefined-time stable and all the signals are bounded in predefined-time interval. Finally, the simulation results are given to confirm the effectiveness of the presented predefined-time control method.

In this article, an adaptive fuzzy tracking control scheme based on a fuzzy state observer is proposed for a class of uncertain, nonstrict feedback, nonlinear systems with function constraints. In the first place, based on the approximation characteristic of fuzzy logic systems (FLSs), a fuzzy state observer is designed to estimate the immeasurable state variables in the controlled system. Next, under the framework of adaptive backstepping control technology, FLSs are selected not only to approximate unknown nonlinear functions but also to avoid the algebraic loop problem caused by nonstrict feedback structure. At the same time, asymmetric Barrier Lyapunov functions are selected to solve the problem that system states are subject to function constraints, which are related to states and time. Then, Lyapunov stability theory is utilized to prove the stability of the controlled system, the realizability of function constraints, and the convergence of output tracking errors. Finally, a simulation is given to check the effectiveness of the proposed control scheme.

In this article, an adaptive tracking control problem is addressed for nonstrict-feedback stochastic nonlinear systems subject to state constraints. Fuzzy logic systems (FLSs) are used to model unknown nonlinearities and avoid the algebraic loop arising from the system structure. Appropriate integral Barrier Lyapunov functions (IBLFs) are chosen so that time-varying full state constraints can be guaranteed directly rather than by transforming the constraint object. In the framework of backstepping technology, the relative threshold strategy is introduced to modify the adaptive control scheme so that the controller can be updated only after the trigger condition has been met, which reduces the update frequency of the controller and the loss of the actuator. Combined with Lyapunov stability theory, it is shown that all closed-loop signals are bounded in probability, in which the states remain within the specified constraints, and there is no Zeno behavior. A series of simulation results are given to reveal the effectiveness of the constructed control scheme.

An adaptive fuzzy-based event-triggered control (ETC) scheme is putted forward in this article, targeted at multi-input multioutput switched nonlinear systems with the situation of control directions are unknown. By designing a state observer and by means of fuzzy logic system, the unmeasurable state and unknown nonlinear function is resolved. The command filter is introduced to backstepping design process, combine with the Nussbaum function technology, overcome the trouble of calculation explosion derived from the partial derivative of the virtual controller, and also solves the influence of unknown control directions on the controller design. By construct multiple Lyapunov functions and under the designed ETC mechanism, an adaptive ETC scheme is developed. In addition, the stability of the system is verified by combining the average dwell time method. Finally, a numerical simulation verification example is given.

This article investigates the problem of fuzzy adaptive asymptotic tracking control for a third-order heterogeneous vehicular platoon system with input saturation. The unknown nonlinear functions are approximated using fuzzy logic systems. To address the issue of input saturation, a control scheme with an auxiliary design system is proposed. A spacing error is created to reduce the intervehicle spacing. The proposed adaptive asymptotic tracking control design scheme employs the barrier Lyapunov functions to impose distance restrictions, ensuring collision avoidance, and maintaining communication connections. The scheme guarantees asymptotic convergence with zero spacing error and proves the individual and string stability of the entire heterogeneous vehicular platoon. Simulations are conducted to demonstrate the effectiveness of the proposed results.

In this article, the research on fixed-time tracking control problem of multiple-input multiple-output nonlinear systems with nonstrict feedback control structure is carried out. By means of the fuzzy logic systems, the unknown system nonlinear dynamics are identified, and the “algebraic loop problem” is solved. Then, through the combination of adaptive backstepping recursive technology and adding power integration technology, a nonsingular fixed-time adaptive tracking control scheme is presented. Under the action of the presented control scheme, the system can track the specified reference signal within a fixed time independent of the initial state of the system, and the tracking control error can converge to zero asymptotically. Next, on the basis of the fixed-time Lyapunov stability theory, the practical fixed-time stability of the closed-loop system is theoretically demonstrated. Finally, two simulations verify the validity and practicability of the proposed control scheme.

This article considers the finite-time containment output-feedback control problem for a class of nonlinear multiagent systems with unmeasurable states and input saturation. Fuzzy logic systems and a smooth function are first employed to model unknown agent's subsystems and input saturation, respectively. Then, a novel fuzzy state observer is established via the intermittent output signal. By introducing the first-order filter and using the sampled estimating states and triggered output signals, an event-triggered mechanism consisting of the sensor-to-controller and controller-to-actuator is formulated. Consequently, under the framework of the finite-time stability criterion and adaptive backstepping control design technique, a finite-time adaptive fuzzy event-triggered output-feedback containment control design method is proposed and the semiglobal finite-time stability of the controlled system is rigorously proved. Finally, the simulation results are given to confirm the effectiveness of the proposed control scheme.

This article investigates the finite-time adaptive fuzzy prescribed performance formation control problem for high-order nonlinear multiagent systems. Fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics. By combining the dynamic surface control technique and backstepping recursive design, an adaptive fuzzy prescribed performance formation control algorithm is developed. To reduce unnecessary transmission of network resources, a novel event-triggered mechanism is proposed in the control method. Subsequently, based on the adding power integral method and finite-time stability theory, it is proved that all signals of the controlled system are bounded and the tracking errors do not exceed the prescribed performance bounds in a finite time. Simulation results are given to verify that the presented formation control scheme achieves desired results.

This article investigates the event-triggered optimized tracking control problem for stochastic nonlinear systems based on reinforcement learning (RL). By using the backstepping strategy, an adaptive RL algorithm is performed under the identifier-critic-actor architecture to achieve event-triggered optimized control (ETOC). Moreover, a novel dynamically adjustable event-triggered mechanism is delicately designed, which adjusts the triggering threshold online to economize communication resources and reduce the computation burden. To overcome the difficulty that the virtual control signals are discontinuous due to the state-triggering, the virtual controllers are designed with the continuous sampling states signals, and the actual optimal controller is redesigned by using the triggered states in the last step. Furthermore, the proposed ETOC in this article has significant advantages in terms of saving network resources because the event-triggered mechanism is employed in the sensor-to-controller channel and the event-sampled states are utilized to directly activate the control actions. Finally, it can be guaranteed that all signals of the stochastic system are bounded under the presented ETOC method. A simulation example is carried out to illustrate the effectiveness of the proposed ETOC algorithm.

In this article, the problem of tracking control for a class of nonlinear time-varying full state constrained systems is investigated. By constructing the time-varying asymmetric barrier Lyapunov function (BLF) and combining it with the backstepping algorithm, the intelligent controller and adaptive law are developed. Neural networks (NNs) are utilized to approximate the uncertain function. It is well known that in the past research of nonlinear systems with state constraints, the state constraint boundary is either a constant or a time-varying function. In this article, the constraint boundaries both related to state and time are investigated, which makes the design of control algorithm more complex and difficult. Furthermore, by employing the Lyapunov stability analysis, it is proven that all signals in the closed-loop system are bounded and the time-varying full state constraints are not violated. In the end, the effectiveness of the control algorithm is verified by numerical simulation.

A robust adaptive control method for a certain type of quarter active suspension system (ASS) is proposed in this work. The constraint issue of ASS is put into consideration primarily. Due to the limitation of the traditional barrier Lyapunov functions (BLFs), the integral barrier Lyapunov function (iBLF) is introduced to exert direct constraints on state variables in each stage under the backstepping frame, and neural networks (NNs) are applied to identify those unknown functions. Then, an adaptive law based on the projection operator is defined to eliminate the influence caused by the actuator failure. It is widely known that only the vertical displacement and velocity constraints are not violated, can the ASSs become stable and secure. It can be ultimately confirmed that all signals in the closed-loop system are bounded, and the control goals are satisfied. Last but not least, the feasibility of the approach is illustrated directly through a contrast simulation example.

In this article, an integral barrier Lyapunov-function (IBLF)-based adaptive tracking controller is proposed for a class of switched nonlinear systems under the arbitrary switching rule, in which the unknown terms are approximated by radial basis function neural networks (RBFNNs). The IBLF method is used to solve the problem of state constraint. This method constrains states directly and avoids the verification of feasibility conditions. In addition, a completely unknown control gain is considered, which makes it impossible to directly apply previous existing methods. To offset the effect of the unknown control gain, the lower bound of the control gain is added into the barrier Lyapunov function, and a regulating term is introduced into the controller. The proposed control strategy realizes three control objectives: 1) all the signals in the resulting system are bounded; 2) the system output tracks the reference signal to a arbitrarily small compact set; and 3) all the constraint conditions for system states are not violated. Finally, a simulation example is used to show the effectiveness of the proposed method.

This article addresses the adaptive tracking control problem for switched uncertain nonlinear systems with state constraints via the multiple Lyapunov function approach. The system functions are considered unknown and approximated by radial basis function neural networks (RBFNNs). For the state constraint problem, the barrier Lyapunov functions (BLFs) are chosen to ensure the satisfaction of the constrained properties. Moreover, a state-dependent switching law is designed, which does not require stability for individual subsystems. Then, using the backstepping technique, an adaptive NN controller is constructed such that all signals in the resulting system are bounded, the system output can track the reference signal to a compact set, and the constraint conditions for states are not violated under the designed state-dependent switching signal. Finally, simulation results show the effectiveness of the proposed method.

In this article, the distributed adaptive neural network (NN) consensus fault-tolerant control (FTC) problem is studied for nonstrict-feedback nonlinear multiagent systems (NMASs) subjected to intermittent actuator faults. The NNs are applied to approximate nonlinear functions, and a NN state-observer is developed to estimate the unmeasured states. Then, to compensate for the influence of intermittent actuator faults, a novel distributed output-feedback adaptive FTC is then designed by co-designing the last virtual controller, and the problem of "algebraic-loop" can be solved. The stability of the closed-loop system is proven by using the Lyapunov theory. Finally, the effectiveness of the proposed FTC approach is validated by numerical and practical examples.

In this article, an anti-attack event-triggered secure control scheme for a class of nonlinear multi-agent systems with input quantization is developed. With the help of neural networks approximating unknown nonlinear functions, unknown states are obtained by designing an adaptive neural state observer. Then, a relative threshold event-triggered control strategy is introduced to save communication resources including network bandwidth and computational capabilities. Furthermore, a quantizer is employed to provide sufficient accuracy under the requirement of a low transmission rate, which is represented by the so-called a hysteresis quantizer. Meanwhile, to resist attacks in the multi-agent network, a predictor is designed to record whether an edge is attacked or not. Through the Lyapunov analysis, the proposed secure control protocol can ensure that all the closed-loop signals remain bounded under attacks. Finally, the effectiveness of the designed scheme is verified by simulation results.

This article presents the adaptive tracking control scheme of nonlinear multiagent systems under a directed graph and state constraints. In this article, the integral barrier Lyapunov functionals (iBLFs) are introduced to overcome the conservative limitation of the barrier Lyapunov function with error variables, relax the feasibility conditions, and simultaneously solve state constrained and coupling terms of the communication errors between agents. An adaptive distributed controller was designed based on iBLF and backstepping method, and iBLF was differentiated by means of the integral mean value theorem. At the same time, the properties of neural network are used to approximate the unknown terms, and the stability of the systems is proven by the Lyapunov stability theory. This scheme can not only ensure that the output of all the followers meets the output trajectory of the leader but also make the state variables not violate the constraint bounds, and all the closed-loop signals are bounded. Finally, the efficiency of the proposed controller is revealed.

This article addresses the output-feedback decentralized control issue for the fractional-order nonlinear large-scale nonstrict-feedback systems with states immeasurable and unknown dead zones. The unknown nonlinear functions are identified by neural networks (NNs), and immeasurable states are estimated by establishing an NNs' decentralized state observer. The algebraic loop issue is solved by using the property of NN basis functions and designing the fractional-order adaptation laws. In addition, the fractional-order dynamic surface control (FODSC) design technique is introduced in the adaptive backstepping control algorithm to avoid the issue of "explosion of complexity." Then, by treating the nonsymmetric dead zones as the time-varying uncertain systems, an adaptive NNs' output-feedback decentralized control scheme is developed via the fractional-order Lyapunov stability criterion. It is proven that the controlled fractional-order systems are stable, and the tracking and observer errors can converge to a small neighborhood of zero. Two simulation examples are given to confirm the validity of the put forward control scheme.

In this article, the stabilization problem is addressed for a class of reaction–diffusion equation described by a cascaded partial differential equation (PDE)–ordinary differential equation (ODE) system. Because of the inherent unknown nonlinearity and actuator failure existing in the considered system, it is fundamentally different from the systems studied in most related studies. To simplify the stability analysis, the original PDE–ODE cascaded system is redescribed as a new target system by leveraging finite- and infinite-dimensional backstepping techniques. In the newly transformed system, the compensation term in the form of the smoothing function is used to eliminate the influence caused by actuator faults. Then, a novel fault-tolerant control strategy is further developed, which can not only eliminate the influence of uncertainty, but also overcome the difficulties of actuator faults. The system stability and the asymptotic convergence of all states in the original system are proved by applying the Lyapunov function theory. The simulation example shows that the presented control method ensures the realization of the control objectives.

This article deals with an adaptive neural network (NN) formation fault-tolerant control (FTC) issue for nonlinear multiagent systems (MASs) with intermittent actuator faults. Since the controlled MASs contain unknown nonlinear dynamics and unmeasurable states, NNs are applied to model unknown subsystems, and an NN state observer is designed by utilizing intermittent output signals. By the designed state observer and introduced first-order filter technique, a new event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels is constructed. To avoid the virtual controller nondifferentiability problem by using backstepping control theory directly, this article redesign the virtual controller and controller obtained by the backstepping control technique without considering the event-triggered signals. The developed output-feedback formation FTC scheme can guarantee the controlled MASs are semi-globally uniformly ultimately bounded in presence of the unknown states and actuator faults. Finally, a simulation example confirms the effectiveness of the presented theory and approach.

This article considers the collision-free fuzzy output-feedback formation control problem for stochastic nonlinear multiagent systems (MASs) with immeasurable states. The fuzzy state observers are established to estimate the unmeasurable states of MASs, and fuzzy-logic systems (FLSs) are utilized to identify the unknown internal dynamics. The prescribed performance functions (PPFs) are introduced to establish the collision avoidance conditions between the follower agent and its leader agent. Then, a novel collision-free adaptive output-feedback formation controller is constructed by utilizing a suitable error transformation. The presented formation control method can guarantee all the variables of the stochastic nonlinear MASs are bounded in probability and each follower agent and the leader agent are free of collision. Finally, the presented formation control method is applied to the unmanned surface vehicle (USV) systems, and the effectiveness and superiorities are checked by the simulation results and comprehensive comparisons.

In this article, an optimal control scheme against false data injection (FDI) attacks for multiagent systems with unavailable system states is presented. The output data that remains uncorrupted is extracted from a group of output measurements during FDI attacks using a secure preselector. Then, on the basis of the unattacked output data, a state observer is utilized to identify system states. By taking the communication overhead into account, an event-triggered mechanism is employed to alleviate communication burdens. The solution of the optimal control problem related to event-triggered Hamilton–Jacobi–Bellman (HJB) equations is obtained within a simplified adaptive dynamic programming (ADP) framework. The key point is that a single network is introduced to successfully avoid the problem of repeated approximations in traditional dual networks. Note that the weight vectors in the single critic network are adjusted through experience replay (ER), which helps to avoid the restrictive persistence of excitation (PE) conditions. It is strictly proven that all the signals in the closed-loop system are uniformly ultimately bounded, and the critic network weight can converge to optimal values. Simulation results illustrate the effectiveness of the control scheme.

In this paper, a class of flexible riser systems modeled by partial differential equations (PDEs) with the backlash is considered. The backlash is formulated as the addition of a linear input and a interference-like term, then an new auxiliary item is introduced to compensate for the impact of this backlash. In addition, the constraint problem for the position and the velocity is also taken into consideration. To solve this constrain problem, the logarithmic barrier Lyapunov function is employed. For the flexible riser system, two kinds of adaptive controllers are proposed under the following two cases. One controller is designed when only the parameter of backlash is unknown. On the basis of this result, the other controller is presented when some system parameters cannot be measured through actual measurement. Then, combing the theory of Lyapunov stability, the two controllers can guarantee the boundedness of all signals in the closed-loop flexible riser system. Further, both the position and the velocity satisfy their corresponding constraint condition. Finally, the simulation example verifies that the proposed control method is effective.

In this article, an adaptive sliding-mode control scheme is developed for a class of uncertain quarter vehicle active suspension systems with time-varying vertical displacement and speed constraints, in which the input saturation is considered. The integral terminal SMC is adopted to improve convergence accuracy and avoid singular problems. In addition, neural networks are used to model unknown terms in the system and the backstepping technique is taken into account to design the actual controller. To guarantee that the time-varying state constraints are not violated, the corresponding Barrier Lyapunov functions are constructed. At the same time, a continuous differentiable asymmetric saturation model is developed to improve the stability of the system. Then, the Lyapunov stability theory is used to verify that all signals of the resulting system are semi globally uniformly ultimately bounded, time-varying state constraints are not violated, and error variables can converge to the small neighborhood of 0. Finally, results of the simulation of the designed control strategy are given to further prove the effectiveness.

This article investigates the model-free containment control of multiple underactuated unmanned surface vessels (USVs) subject to unknown kinetic models. A novel cooperative control architecture is presented for achieving a containment formation under switching topologies. Specifically, a path-guided distributed containment motion generator (CMG) is first proposed for generating reference points according to the underlying switching topologies. Next, guiding-vector-field-based guidance laws are designed such that each USV can track its reference point, enabling smooth transitions during topology switching. Finally, data-driven neural predictors by utilizing real-time and historical data are developed for estimating total uncertainties and unknown input gains, simultaneously. Based on the learned knowledge from neural predictors, adaptive kinetic control laws are designed and no prior information on kinetic model parameters is required. By using the proposed method, the fleet is able to converge to the convex hull spanned by multiple virtual leaders under switching topologies regardless of fully unknown kinetic models. Through stability analyses, it is proven that the closed-loop control system is input-to-state stable and the tracking errors are uniformly ultimately bounded. Simulation results verify the effectiveness of the proposed cooperative control architecture for multiple underactuated USVs with fully unknown kinetic models.

This article investigates the adaptive neural-network (NN) tracking optimal control problem for stochastic nonlinear systems, which contain state constraints and uncertain dynamics. First, to avoid the violation of state constraints in achieving optimal control, the novel barrier optimal performance index functions for subsystems are developed. Second, under the framework of the identifier-actor-critic, the virtual and actual optimal controllers are presented based on the backstepping technique, in which the unknown nonlinear dynamics are learned by the NN approximators. Moreover, the quartic barrier Lyapunov functions are constructed instead of square ones to cope with the Hessian term to ensure the stability of the systems with stochastic disturbance. The proposed optimal control strategy can guarantee the boundedness of closed-loop signals, and the output can follow the given reference signal. Meanwhile, the system states are restricted within some preselected compact sets all the while. Finally, both numerical and practical systems are carried out to further illustrate the validity of the proposed optimal control approach.

The adaptive fuzzy tracking control problems for a class of uncertain stochastic nonlinear systems are investigated in this article using the backstepping control approach. Different from the existing research, the crucial but highly restrictive hypothesis on the prior knowledge of unknown virtual control coefficients (UVCCs) is removed from this article. An asymptotic tracking control scheme is proposed by applying smooth functions and a bounded estimation method. By delicately constructing a specific composite Lyapunov function for the controlled system and several useful inequalities, the stability and asymptotic tracking performance with unknown nonlinear function and unknown UVCCs can be guaranteed almost surely. Finally, the method is illustrated with simulation examples.

This article addresses the finite-time event-triggered adaptive neural control for fractional-order nonlinear systems. Based on the backstepping technique, a novel adaptive event-triggered control scheme is proposed, and finite-time stability criteria are introduced with the aim to ensure that the tracking error enters into a small region around the origin in finite time. Finally, the stability of the closed-loop system is ensured via a fractional Lyapunov function theory and two simulation examples were used to prove the validity of the designed control scheme.

This article studies the adaptive fuzzy output-feedback decentralized control problem for the fractional-order nonlinear large-scale systems. Since the considered strict-feedback systems contain unknown nonlinear functions and unmeasurable states, the fuzzy-logic systems (FLSs) are used to model unknown fractional-order subsystems, and a fuzzy decentralized state observer is established to obtain the unavailable states. By introducing the dynamic surface control (DSC) design technique into the adaptive backstepping control algorithm and constructing the fractional-order Lyapunov functions, an adaptive fuzzy output-feedback decentralized control scheme is developed. It is proved that the decentralized controlled system is stable and that the tracking and observer errors are able to converge to a neighborhood of zero. A simulation example is given to confirm the validity of the proposed control scheme.

This article addresses a new adaptive fuzzy fast finite-time state-constraint protocol for leader-follower formation control. Each agent in uncertain nonlinear dynamic multiagent systems is represented by second-order integrator, which synchronously governs its position and velocity. The fuzzy logic systems are employed to compensate and approximate uncertain functions. On the premise of maintaining formation structure and coupling communication topology, time-varying transformation equations containing exponential signals are introduced to ensure that state capability boundaries for different physical quantities of agents are not violated. It not only guarantees own state performance and collision avoidance among agents, but also realizes the specified transient and steady formation performance. Furthermore, focusing on convergence rate, the adaptive fuzzy fast finite-time strategy is designed that can guarantee all agents will follow the desired formation configuration in fast finite-time. Through the abovementioned approaches provide a good way to improve the convergence and ensure the security for decentralized formation control. Finally, the validity of the theoretical method is proved by fast finite-time stable theory and Lyapunov stability theory. The effectiveness of the protocol is verified by digital simulation and simulation comparison.

This article investigates the problem of fuzzy adaptive consensus tracking control for nonlinear multiagent systems with unknown nonlinear control gain functions. In the control design, fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and a distributed state observer is constructed to estimate the unmeasured states. Under the case of directed graph, by constructing the logarithm Lyapunov functions, an adaptive fuzzy distributed control method is presented, which removes the restrictive assumptions about the unknown control gain functions must be constants in traditional adaptive intelligent output feedback control methods. The developed control scheme cannot only ensure that all signals of the controlled system are semiglobal uniformly ultimately bounded, but also make the outputs of all the followers keep consensus with the output trajectory of the leader. Finally, simulation results are given to illustrate the effectiveness of the developed consensus control scheme and theorem.

The finite-time dynamic event-triggered fuzzy output feedback fault-tolerant control problem is studied in this article for the interval type-2 (IT2) Takagi–Sugeno fuzzy system with parameter uncertainties and actuator faults. A fuzzy state observer is first developed to solve the immeasurable state problem. Second, by using the sampled estimating states and measured output signals, a dynamic event-triggered mechanism is formulated via integrating sensor-to-observer with observer-to-controller. Third, an observer-based finite-time event-triggered fuzzy fault-tolerant controller is synthesized via the nonparallel distribution compensation design principle. Consequently, the finite-time stable conditions of the addressed IT2 fuzzy system are established by constructing an appropriate Lyapunov function. Furthermore, an output feedback control design algorithm of solving control and observer gains is given in terms of the established sufficient finite-time stable conditions. Finally, a practical example of a nonlinear tunnel diode circuit system is provided to verify the effectiveness of the proposed IT2 fuzzy control scheme.

In this article, a fuzzy adaptive output feedback control strategy is designed for a class of uncertain nonlinear switched system with full state constraints under arbitrary switching signal. The states of the system studied in this article are unmeasurable, so a fuzzy observer is designed to estimate the unmeasurable states. At the same time, in order to ensure that the states of the system do not violate the constraints related to the desired output and states, the log-type barrier Lyapunov function method is selected to solve this constraint problem. Finally, through Lyapunov stability theory analysis, it is found that the designed control strategy can ensure that all signals in the closed-loop system are bounded, and the states of the system do not violate their corresponding constraints. In addition, a numerical simulation verifies the effectiveness of the control strategy.

In this article, the high-order nonlinear system is commonly studied in an underactuated weakly coupled mechanical system, the control design is difficult from the tractional control design for nonlinear systems. Thus, we study the finite-time fuzzy adaptive error constraint control problem for stochastic high-order nonlinear nonstrict feedback systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, a new error transfer variable is used to achieve the prescribed performance. Based on adding a power integrator technique and adaptive backstepping recursive control, a novel adaptive fuzzy finite-time prescribed performance control scheme is developed. By utilizing stochastically finite-time stable theory, the proposed control method can guarantee that the high-order system is semi-global finite-time stable in probability. Finally, both numerical and practical simulations are provided to verify the feasibility and effectiveness of the developed control method.

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided.

This article investigates the fixed-time adaptive fuzzy containment control problem for nonlinear multiagent systems under the directed communication topologies. The controlled systems have the unknown internal dynamics and mismatched disturbances, and fuzzy logic systems are utilized to identify the unknown internal dynamics. The mismatched disturbances and approximate errors are reconstructed via a disturbance observer. Then, by introducing an adding power integral method, a fixed-time adaptive fuzzy containment DSC scheme is developed to deal with the problem of “computation complexity.” The presented containment control method can not only guarantee that the controlled system is semiglobal practical fixed-time stable, but also avoid the “singular problem” in fixed-time backstepping recursive control technology. Finally, an application of marine surface vehicle is provided to verify the effectiveness of the presented fixed-time fuzzy containment control method.

In this article, an adaptive tracking control approach is developed for a class of strict-feedback nonlinear systems with time-varying full state constraints. As a breakthrough in this system, the special function constraints (whose constraint boundary is relevant to both state variables and time) are considered, which are rarely studied by research work. And there is no doubt that this method increases the complexity of designing this scheme. Furthermore, the time-varying integral barrier Lyapunov functions combining with backstepping technique is introduced to break the limitation of traditional methods as well as achieve the full state constraints. Meanwhile, fuzzy logic systems are selected to approximate unknown nonlinear functions. It is verified that all closed-loop signals are bounded and all states are forced in the time-varying boundness. In addition, the proposed control strategy has a good performance. The effectiveness of the theoretical analysis results is proved via a simulation example.

The aim of this article is to study a fuzzy-based decentralized adaptive control strategy for the nonstrict-feedback fractional-order nonlinear large-scale systems with unknown control directions. In each step of the recursive processes, the fuzzy logic systems are employed to identify unknown nonlinear functions. To handle the difficulties caused by unknown control directions, a Nussbaum function technique is adopted. Furthermore, by introducing the dynamic surface control technique into the adaptive backstepping recursive design algorithm, a fuzzy-based decentralized adaptive control strategy is formulated. Both the stability of the controlled system and the convergence of the tracking errors are proved by constructing the fractional-order Lyapunov functions. Finally, the validity and effectiveness of the designed decentralized control scheme are confirmed via two simulation examples.

This article studies the fuzzy adaptive finite-time consensus control problem for high-order nonlinear multiagent systems with unknown nonlinear dynamics. In control design,fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and under the frameworks of adaptive backstepping recursive design and finite-time stability theory, an adaptive fuzzy finite-time consensus control method is developed. To save communication resources and reduce the numbers of controller execution times, a dynamic event-triggered mechanism with a relative threshold is established. Subsequently, an event-triggered-based finite-time fuzzy adaptive control scheme is formulated. Furthermore, by constructing novel integral-type Lyapunov functions and adding a power integrator technique, the finite-time stability of the closed-loop system and the convergence of consensus tracking errors are proved. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed adaptive event-triggered consensus control method.

In this article, an adaptive optimized formation control problem is studied for the second-order stochastic multiagent systems (MASs) with unknown nonlinear dynamics. Compared with first-order formation control, the second-order MASs consider not only the states but also the states rates, which is certainly more challenging and difficult work. In the control design of this article, the fuzzy logic systems are applied to approximate the nonlinear functions. By employing the actor-critic architecture and Lyapunov stability theory, the proposed optimal formation control strategy ensures that all the error signals are bounded in probability. Finally, the simulation examples verify that the proposed formation control approach achieves desired results.

This article concentrates on the event-driven controller design problem for a class of nonlinear single input single output parametric systems with full state constraints. A varying threshold for the triggering mechanism is exploited, which makes the communication more flexible. Moreover, from the viewpoint of energy conservation and consumption reduction, the system capability becomes better owing to the contribution of the proposed event-triggered mechanism. In the meantime, the developed control strategy can avoid the Zeno behavior since the lower bound of the sample time is provided. The considered plant is in a lower triangular form, in which the match condition is not satisfied. To ensure that all the states retain in a predefined region, a barrier Lyapunov function (BLF) based adaptive control law is developed. Due to the existence of the parametric uncertainties, an adaptive algorithm is presented as an estimated tool. All the signals appearing in the closed-loop systems are then proven to be bounded. Meanwhile, the output of the system can track a given signal as far as possible. In the end, the effectiveness of the proposed approach is validated by an aircraft wing rock motion system.

A novel adaptive control scheme is developed for active suspension systems (ASSs) based on neural networks (NNs) and backstepping control strategies. Since the springs and piecewise dampers are nonlinear, the unknown internal dynamics are approximated by radial basis function neural networks (RBFNNs). Then, to solve the time-varying constrains of both vertical displacement and corresponding speed in vehicle body, the Tangent Barrier Lyapunov Functions (TBLFs) are incorporated into the controller design. Furthermore, the adaptive controller and adaptive laws are designed to improve the riding comfortable, handling stability and driving safety. In the end, the simulation results show the effectiveness and feasibility of the proposed adaptive algorithm compared with unconstrained adaptive approach.

This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.

In this article, the adaptive neural backstepping control approaches are designed for uncertain stochastic nonlinear systems with full-state constraints. According to the symmetry of constraint boundary, two cases of controlled systems subject to symmetric and asymmetric constraints are studied, respectively. Then, corresponding adaptive neural controllers are developed by virtue of backstepping design procedure and the learning ability of radial basis function neural network (RBFNN). It is worth mentioning that the integral Barrier Lyapunov function (IBLF), as an effective tool, is first applied to solve the above constraint problems. As a result, the state constraints are avoided from being transformed into error constraints via the proposed schemes. In addition, based on Lyapunov stability analysis, it is demonstrated that the errors can converge to a small neighborhood of zero, the full states do not exceed the given constraint bounds, and all signals in the closed-loop systems are semiglobally uniformly ultimately bounded (SGUUB) in probability. Finally, the numerical simulation results are provided to exhibit the effectiveness of the proposed control approaches.

In this work, an adaptive neural network (NN) optimized output-feedback control problem is studied for a class of stochastic nonlinear systems with unknown nonlinear dynamics, input saturation, and state constraints. A nonlinear state observer is designed to estimate the unmeasured states, and the NNs are used to approximate the unknown nonlinear functions. Under the framework of the backstepping technique, the virtual and actual optimal controllers are developed by employing the actor-critic architecture. Meanwhile, the tan-type Barrier optimal performance index functions are developed to prevent the nonlinear systems from the state constraints, and all the states are confined within the preselected compact sets all the time. It is worth mentioning that the proposed optimized control is clearly simple since the reinforcement learning (RL) algorithm is derived based on the negative gradient of a simple positive function. Furthermore, the proposed optimal control strategy ensures that all the signals in the closed-loop system are bounded. Finally, a practical simulation example is carried out to further illustrate the effectiveness of the proposed optimal control method.

The adaptive neural network (NN) output-feedback optimal control issue has been investigated for a quarter-car active electric suspension systems, where the suspension stiffness is unknown and partial state variables are unavailable for measurement. NNs are utilized to identify unknown nonlinearities, and an NN state observer is devised to estimate the unmeasurable states. For each backstepping step, via reinforcement learning (RL), a critic–actor architecture is designed to get the approximation solution of Hamilton–Jacobi–Bellman (HJB) equations and actual and virtual optimization controllers are designed, in which the input saturation constraint and road interference are considered. It is analytically proved that all controlled system signals remain bounded, while the power of the control input signal, as well as the amplitude of the vertical displacement, has been minimized. A comparative simulation is eventually given to elaborate the feasibility of the developed control algorithm.

This article investigates optimal control problem for a class of discrete-time (DT) nonlinear systems with unknown dynamics. With the help of a broad learning system (BLS), a novel online adaptive dynamic programming (ADP) controller is presented. First, to approximate the unknown system dynamics, an approximator based on BLS is presented. The connection weights are calculated by the data of the system by using the ridge regression algorithm. Then, two BLSs are adopted to approximate the optimal cost function and optimal control law, respectively. The connection weights of these two BLSs are updated using the given weights tuning law at each sampling instant. The proposed optimal controller is proved to ensure that all the system states and estimation errors are uniform ultimate bounded. Finally, simulation examples are carried out to further demonstrate the effectiveness of the proposed BLS-based approximator and optimal controller.

In this article, the finite-time fault-tolerant control (FTC) problem is investigated for uncertain nonlinear nonstrict-feedback systems. The nonstrict-feedback nonlinear system considered in this article contains unmeasured states, unknown control directions, unknown nonlinear dynamics, and actuator faults (both lock-in-place and loss of effectiveness). To realize the control objective, fuzzy-logic systems are used to approximate the unknown nonlinear functions, and a high-gain fuzzy state observer is developed. By using the Nussbaum function technique and combining with the adaptive backstepping control design, a fuzzy adaptive finite-time output-feedback FTC scheme is proposed. It is proved that the closed-loop system is practical finite-time stable (PFTS), and the system output can track a given reference signal. Simulation and comparison results further show the effectiveness of the proposed control strategy.

Aiming at a class of switched uncertain nonlinear strict-feedback systems under the action of average dwell time switching signal, this paper proposes a novel adaptive neural network output feedback tracking control based on the consideration of the full state constraints. The controller is proposed based on neural networks. One of the key characteristics of the system discussed is that the state variables cannot be measured and the system states need to be kept within the constraint ranges. For the sake of estimating the unmeasured states, the observer is constructed. In order to ensure all states which are within the time-varying boundary, the tangent barrier Lyapunov function (BLF-Tan) is selected in the design process. The boundedness of the closed-loop signals with average dwell time is guaranteed by the designed controllers and all the states limit in their constrained sets. It has been proved that the output tracking error converge to a small neighborhood of zero. In addition, the significance of the presented control strategy is verified and tested by a simulation example.

In this paper, an adaptive neural network (NN) control scheme is developed for a class of stochastic nonlinear systems with time-varying full state constraints. In the controller design, RBF NNs are employed to approximate the unknown terms, and the backtracking technique is introduced to overcome the restriction of matching conditions. At the same time, tangent type time-varying barrier Lyapunov functions (tan-TVBLFs) are constructed to ensure the full state constraints are never violated, where tan-TVBLFs are beneficial to integrate constraint analysis into a common method. Furthermore, the Lyapunov stability theory is used to prove that all closed-loop signals are semiglobal uniformly ultimately bounded in probability and error signals remain in the compact set do not violate the time-varying constraints. A simulation example will be used to exhibit the effectiveness of the proposed control scheme.

This article is concerned with the finite-time containment control problem for nonlinear multiagent systems, in which the states are not available for control design and the control input contains time delay. Fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear functions and a novel distributed fuzzy state observer is proposed to obtain the unmeasured states. Under the framework of cooperative control and finite-time Lyapunov function theory, an observer-based adaptive fuzzy finite-time output-feedback containment control scheme is developed via the adaptive backstepping control design algorithm and integral compensator technique. The proposed adaptive fuzzy containment control method can ensure that the closed-loop system is stable and all followers can converge to the convex hull built by the leaders in finite time. A simulation example is provided to confirm the effectiveness of the proposed control method.

This article presents an adaptive output feedback approach of nonlinear multi-input-multi-output (MIMO) systems with time-varying state constraints and unmeasured states. An adaptive approximator is designed to approximate the unknown nonlinear functions existing in the state-constrained systems with immeasurable states. To deal with the tracking problem of such systems, a state observer with time-varying barrier Lyapunov functions (BLFs) is introduced in the controller design procedure. The backstepping design with time-varying BLFs is utilized to guarantee that all system states remain within the time-varying-constrained interval. The constant constraint is only the special case of the time-varying constraint which is more general in the real systems. The proposed control approach guarantees that all signals in the closed-loop systems are bounded and the tracking errors converge to a bounded compact set, and time-varying full-state constraints are never violated. A simulation example is given to confirm the feasibility of the presented control approach in this article.

This article is concerned with the adaptive event-triggered control (ETC) problem for uncertain nonlinear systems with full state constraints. By combining the asymmetric barrier Lyapunov functions with the backstepping technique, an adaptive ETC method is designed for the system under consideration. In addition, by introducing some well-defined smooth functions and the bounded estimation approach, the effects caused by the unknown virtual control coefficients and unknown nonlinear functions are counteracted. The asymptotic stability of the closed-loop system is ensured without violating the state constraints. Finally, the effectiveness of the control method is evaluated through simulations.

This article proposes an adaptive fuzzy controller for a class of uncertain strict-feedback nonmatching nonlinear single-input single-output systems with fuzzy dead zone and full time-varying state constraints. The states considered here are immeasurable and full states of the systems are constrained in a bounded set with time-varying regions. Following the adaptive backstepping design framework, the tangent barrier Lyapunov functions are introduced to the integrated design to address the problems in such systems. Fuzzy logic systems are used to identify the unknown smooth functions and unknown parameters. An input-driven observer is designed to estimate the immeasurable states. To distinguish the conventional deterministic dead zone models, the output of dead zone is uncertainty. The form of indeterminate dead zone as a combination of a liner and a disturbance-like term is extended by the fuzzy algorithms. Even though the output of dead zone is fuzzy and adopting the integrated design, the proposed fuzzy controller can ensure that all the signals in the closed-loop systems are semiglobal uniformly ultimately bounded and guarantee the tracking performance. Finally, simulation results are shown to verify the effectiveness and reliability of the proposed approach.

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

This article investigates the problem of finite-time fuzzy adaptive event-triggered control design for stochastic nonlinear nonstrict feedback systems with unmodeled dynamics. The fuzzy logic systems are adopted to identify the unknown nonlinearities and a state observer is designed to estimate the unmeasured states. Using backstepping recursive design and combining it with a varying threshold event-triggered condition, a novel event-triggered-based fuzzy adaptive finite-time control algorithm is developed, where the dynamical signal function is employed to deal with the unmodeled dynamics. A power form of the errors is used to ensure a continuous stabilizer. The semi-global finite-time stability in probability of the closed-loop system is proved based on an It∧o differential equation and finite-time stability theory. Simulations are provided to verify the effectiveness of the developed control algorithm.

This article studies the problem of the robust fuzzy adaptive finite-time control design for a class of single-input single-output high-order nonlinear systems. The considered plants contain unknown nonlinear functions, unmodeled dynamics, and dynamical disturbances. In this control design, fuzzy logic systems are utilized to approximate unknown nonlinear functions, and dynamical signal functions are introduced to solve unmodeled dynamics and dynamical disturbances. Under the framework of an adaptive backstepping control and adding a power integrator control design technique, a robust fuzzy adaptive finite-time control scheme is developed, which can not only guarantee the controlled system to be semiglobal practical finite-time stable, but also have the robustness to unmodeled dynamics and dynamical disturbances. Both numerical and practical simulation examples are provided to check the effectiveness of the proposed control method.

This article investigates an adaptive finite-time neural control for a class of strict feedback nonlinear systems with multiple objective constraints. In order to solve the main challenges brought by the state constraints and the emergence of finite-time stability, a new barrier Lyapunov function is proposed for the first time, not only can it solve multiobjective constraints effectively but also ensure that all states are always within the constraint intervals. Second, by combining the command filter method and backstepping control, the adaptive controller is designed. What is more, the proposed controller has the ability to avoid the "singularity" problem. The compensation mechanism is introduced to neutralize the error appearing in the filtering process. Furthermore, the neural network is used to approximate the unknown function in the design process. It is shown that the proposed finite-time neural adaptive control scheme achieves a good tracking effect. And each objective function does not violate the constraint bound. Finally, a simulation example of electromechanical dynamic system is given to prove the effectiveness of the proposed finite-time control strategy.

This article investigates the problem of neural network (NN)-based adaptive backstepping control design for stochastic nonlinear systems with unmodeled dynamics in finite-time prescribed performance. NNs are used to study the uncertain control plants, and the problem of unmodeled dynamics is tackled by the combination of the changing supply function and the dynamical signal function methods. The outstanding contribution of this article is that based on the finite-time performance function (FTPF), a modified finite-time adaptive NN control design strategy is proposed, which makes the controller design simpler. Eventually, by using the Itô's differential lemma, the backstepping recursive design technique, and the FTPFs, a novel adaptive prescribed performance tracking control scheme is presented, which can guarantee that all the variables in the control system are bounded in probability, and the tracking error can converge to a specified performance range in the finite time. Finally, both numerical simulation and applied simulation examples are provided to verify the effectiveness and applicability of the proposed method.

Due to the particularity of the fractional-order derivative definition, the fractional-order control design is more complicated and difficult than the integer-order control design, and it has more practical significance. Therefore, in this article, a novel adaptive switching dynamic surface control (DSC) strategy is first presented for fractional-order nonlinear systems in the nonstrict feedback form with unknown dead zones and arbitrary switchings. In order to avoid the problem of computational complexity and to continuously obtain fractional derivatives for virtual control, the fractional-order DSC technique is applied. The virtual control law, dead-zone input, and the fractional-order adaptive laws are designed based on the fractional-order Lyapunov stability criterion. By combining the universal approximation of neural networks (NNs) and the compensation technique of unknown dead-zones, and stability theory of common Lyapunov function, an adaptive switching DSC controller is developed to ensure the stability of switched fractional-order systems in the presence of unknown dead-zone and arbitrary switchings. Finally, the validity and superiority of the proposed control method are tested by applying chaos suppression of fractional power systems and a numerical example.

In this article, an adaptive neural network (NN) decentralized output-feedback control design is studied for the uncertain strict-feedback large-scale interconnected nonlinear systems with nonconstant virtual and control gains. NNs are utilized to approximate the unknown nonlinear functions, and the immeasurable states are estimated via designing an NN decentralized state observer. By constructing the logarithm Lyapunov functions, an observer-based NN adaptive decentralized backstepping output-feedback control is developed in the framework of the decentralized backstepping control. The proposed adaptive decentralized backstepping output-feedback control can make that the closed-loop system is semiglobally uniformly ultimately bounded (SGUUB) and that the tracking and observer errors converge to a small neighborhood of the origin. The most important contribution of this article is that it removes the restrictive assumption in the existing results that both virtual and control gain functions in each subsystem must be constants. A numerical simulation example is provided to validate the effectiveness of the proposed control method and theory.

The event-triggered consensus control problem is studied for nonstrict-feedback nonlinear systems with a dynamic leader. Neural networks (NNs) are utilized to approximate the unknown dynamics of each follower and its neighbors. A novel adaptive event-trigger condition is constructed, which depends on the relative output measurement, the NN weights estimations, and the states of each follower. Based on the designed event-trigger condition, an adaptive NN controller is developed by using the backstepping control design technique. In the control design process, the algebraic loop problem is overcome by utilizing the property of NN basis functions and by designing novel adaptive parameter laws of the NN weights. The proposed adaptive NN event-triggered controller does not need continuous communication among neighboring agents, and it can substantially reduce the data communication and the frequency of the controller updates. It is proven that ultimately bounded leader-following consensus is achieved without exhibiting the Zeno behavior. The effectiveness of the theoretical results is verified through simulation studies.

This paper studies the adaptive control problem for a class of uncertain fractional nonlinear systems with actuator faults, where the total number of failures is allowed to be infinite. A compensating term in a smooth function form of a conventional control law is introduced to compensate for the actuator faults. After the introduction of fractional-order adaptation laws, an adaptive controller is designed by using a modified backstepping technique. Fractional Lyapunov stability criterion is adopted to prove the convergence of the developed proposed controller even in the presence of actuator faults. Finally, a simulation example of fractional-order Chua-Hartley's system is given to verify the effectiveness of the proposed fault-tolerant control scheme.

In this article, a novel fuzzy adaptive tracking control scheme is concerned for a class of stochastic state-constrained switched nonlinear systems. The considered stochastic switched nonlinear system contains unknown nonlinearities and unstable inverse dynamics. In the design process, first, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear dynamics. Second, the stochastic barrier Lyapunov functions (BLFs) are constructed to deal with the state constraint problem. Then, an adaptive fuzzy state-feedback controller is designed by utilizing the It∧o lemma and average dwell time (ADT) approach, which can guarantee both the control system and unstable inverse dynamics to be bounded in probability and all the states cannot violate their constrained sets. Two simulation examples are provided to show the effectiveness of the proposed control approach.

This article investigates an adaptive reinforcement learning (RL) optimal control design problem for a class of nonstrict-feedback discrete-time systems. Based on the neural network (NN) approximating ability and RL control design technique, an adaptive backstepping RL optimal controller and a minimal learning parameter (MLP) adaptive RL optimal controller are developed by establishing a novel strategic utility function and introducing external function terms. It is proved that the proposed adaptive RL optimal controllers can guarantee that all signals in the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). The main feature is that the proposed schemes can solve the optimal control problem that the previous literature cannot deal with. Furthermore, the proposed MPL adaptive optimal control scheme can reduce the number of adaptive laws, and thus the computational complexity is decreased. Finally, the simulation results illustrate the validity of the proposed optimal control schemes.

This paper addresses the decentralized output feedback problem of an interconnected nonlinear system subject to uncertain interactions. A decentralized event-triggered control scheme is presented so that the decentralized output feedback problem is solved with only event-sampling states. With the proposed triggering mechanism, each subsystem only uses local signals to construct the decentralized controller at its own triggering times or the switching times. It is proved that both the tracking performance and the closed-loop stability can be preserved via the presented approach. Moreover, a uniform positive lower bound for the interevent time is guaranteed. Simulation results are presented to illustrate the effectiveness of the proposed control design.

In this article, the adaptive fault-tolerant control (FTC) problem is solved for a switched resistance-inductance-capacitance (RLC) circuit system. Due to the existence of faults which may lead to instability of subsystems, the innovation of this article is that the unstable subsystems are taken into account in the frame of output constraint and unmeasurable states. Obviously, there are not any unstable subsystems in unswitched systems. The unstable subsystems will involve many serious consequences and difficulties. Since the system states are unavailable, a switched state observer is designed. In addition, the fuzzy-logic systems (FLSs) are employed to approximate unknown internal dynamics in the controller design procedure. Then, the barrier Lyapunov function (BLF) is exploited to guarantee that the system output satisfy its constrained interval. Moreover, by using the average dwell-time method, all signals in the resulting systems are proofed to be bounded even when faults occur. Finally, the proposed strategy is carried out on the switched RLC circuit system to show the effectiveness and practicability.

This article investigates the adaptive fuzzy output-feedback backstepping control design problem for uncertain strict-feedback nonlinear systems in the presence of unknown virtual and actual control gain functions and unmeasurable states. A fuzzy state observer is designed via fuzzy-logic systems, thus the unmeasurable states are estimated based on the designed fuzzy state observer. By constructing the logarithm Lyapunov functions and incorporating the property of the fuzzy basis functions and bounded control design technique into the adaptive backstepping recursive design, a novel observer-based adaptive fuzzy output-feedback control method is developed. The proposed fuzzy adaptive output-feedback backstepping control scheme can remove the restrictive assumptions in the previous literature that the virtual control gains and actual control gain functions must be constants. Furthermore, it can make the control system be semiglobally uniformly ultimately boundedness (SGUUB) and keep the observer and tracking errors to remain in a small neighborhood of the origin. The numerical simulation example is presented to validate the effectiveness of the proposed control scheme and theory.

In this paper, the adaptive fuzzy event-triggered containment control problem is addressed for uncertain nonlinear strict-feedback systems guided by multiple leaders. A novel distributed adaptive fuzzy event-triggered containment control is designed only using the information of the individual follower and its neighbors. Moreover, a distributed event-trigger condition with an adjustable threshold is developed simultaneously. The designed containment control law is updated in an aperiodic manner, only when event-triggered errors exceed tolerable thresholds. It is proved that the uniformly ultimately bounded containment control can be achieved, and there is no Zeno behavior exhibited by applying the proposed control scheme. Simulation studies are outlined to illustrate the effectiveness of the theoretical results and the advantages of the event-triggered containment control proposed in this paper.

This article first investigates the adaptive fuzzy inverse optimal control design problem for a class of uncertain strict-feedback nonlinear systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, and then, an equivalent system and an auxiliary system are established. Based on the auxiliary system and using backstepping recursive design algorithm, an adaptive fuzzy inverse optimal scheme, associating with a meaningful objective functional, is developed. It is proved that the presented adaptive fuzzy inverse optimal control scheme can guarantee that the considered system is input-to-state stabilizable and also achieves the goal of inverse optimality with respect to the cost functional. Finally, the simulation studies and comparisons via two examples are provided to confirm the validity of the developed control strategy.

In this article, a new n-step fuzzy adaptive output tracking prescribed performance control problem is investigated for a class of nontriangular structure nonlinear systems. In the control design process, the mean value theorem is used to separate the virtual state variables needed for the control design, and the implicit function theorem is exploited to assert the existence of the desired continuous control. The fuzzy logic systems are used to identify the unknown nonlinear functions and ideal controller, respectively. By constructing a novel iterative Lyapunov function, a new n-step adaptive backstepping control design algorithm is established. The prominent characteristics of the proposed adaptive fuzzy backstepping control design algorithm are as follows: one is that it can ensure the closed-loop control system is the semiglobally uniformly ultimately bounded and the tracking error can converge within the prescribed performance bounds. The other is that it solves the controller design problem for the nontriangular nonlinear systems that the previous adaptive backstepping design techniques cannot deal with. Two examples are provided to show the effectiveness of the presented control method.

This article is concerned with the adaptive fuzzy event-triggered control for leader-following consensus of high-order nonlinear systems under directed communication topologies. Utilizing fuzzy logic systems to model the uncertain dynamics of the followers, a novel adaptive fuzzy event-triggered control law is presented, and a distributed event-trigger condition is proposed, simultaneously. The developed adaptive fuzzy event-triggered control is carried out by the violation of the designed event-trigger condition, which can realize ultimate state synchronization with bounded tracking errors. Moreover, the data transmissions and the frequency of the control law updates can be significantly reduced compared with the control law with fixed sampling period. In addition, it is proved that the Zeno behavior is excluded in the proposed control scheme. Finally, a simulation example is provided to illustrate the obtained theoretical results.

In this paper, a novel adaptive fuzzy tracking control strategy is developed for nonlinear time-varying delayed systems with full state constraints. State constraints and time delays are normally found in various real-life plants, which are two important factors for degrading system performance significantly. In the framework of adaptive control, the effects of state constraints and time-varying delays are removed simultaneously. The integral Barrier Lyapunov functionals (IBLFs) are applied to achieve full-state-constraint satisfactions and remove the need of the transformed error constraints in previous BLFs. The unknown time-varying delays are completely compensated by introducing the separation technique and Lyapunov–Krasovskii functionals (LKFs). The unknown functions existing in systems are approximated by employing fuzzy logic systems (FLSs). With the help of less-adjustable parameters, only one parameter is needed to be adjusted online in each step of control design. The novel strategy can guarantee that a satisfactory tracking performance is achieved and the signals existing in the closed-loop system are bounded. Finally, by presenting simulation results, the efficiency of the proposed approach is revealed.

This article investigates the adaptive neural network (NN) finite-time output tracking control problem for a class of multi-input and multi-output (MIMO) uncertain nonlinear systems whose powers are positive odd rational numbers. Such designs adopt NNs to approximate unknown continuous system functions, and a controller is constructed by combining backstepping design and adding a power integrator technique. By constructing new iterative Lyapunov functions and using finite-time stability theory, the closed-loop stability has been achieved, which further verifies that the entire system possesses semiglobal practical finite-time stability (SGPFS), and the tracking errors converge to a small neighborhood of the origin within finite time. Finally, a simulation example is given to elaborate the effectiveness and superiority of the developed.

This article addresses the finite-time optimal control problem for a class of nonlinear systems whose powers are positive odd rational numbers. First of all, a finite-time controller, which is capable of ensuring the semiglobal practical finite-time stability for the closed-loop systems, is developed using the adaptive neural networks (NNs) control method, adding one power integrator technique and backstepping scheme. Second, the corresponding design parameters are optimized, and the finite-time optimal control property is obtained by means of minimizing the well-defined and designed cost function. Finally, a numerical simulation example is given to further validate the feasibility and effectiveness of the proposed optimal control strategy.

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified.

This paper investigates an adaptive fuzzy output feedback control design problem for the switched multiple-input and multiple-output (MIMO) nontriangular structure nonlinear systems. The discussed system contains the unknown nonlinear dynamics, the unknown backlash hysteresis, the immeasurable states, and the unknown control directions under a class of switching signals. The fuzzy logic systems are utilized to learn the unknown nonlinear dynamics and construct an MIMO fuzzy switched nonlinear observer. By combining the property of the Nussbaum gain function with the Prandtl-Ishlinskii models, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the whole controlled system is proved via Lyapunov stability theory and the average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme.

This paper addresses the finite time adaptive fuzzy decentralized control problem for interconnected large scale nonlinear systems in nonstrict feedback forms with output-constraint. The fuzzy logic systems are used to approximate the unknown nonlinear functions and a state observer is constructed to estimate the immeasurable states. In order to deal with the output constraint problem, the barrier Lyapunov function is introduced. By combining backstepping recursion design with a command filter, a finite time fuzzy adaptive decentralized control method is presented. The stability analysis can be obtained based on the finite time Lyapunov stability theory, which demonstrates that the closed-loop system are semi-global practical finite-time stability, the system outputs can track the given reference signals and keep in the given constraint bounds in a finite time. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control scheme.

In this paper, an adaptive neural network (NN) controller is proposed for a class of nonlinear active suspension systems (ASSs) with hydraulic actuator. To eliminate the problem of “explosion of complexity” inherently in the traditional backstepping design for the hydraulic actuator, a dynamic surface control technique is developed to stabilize the attitude of the vehicle by introducing a first-order filter. Meanwhile, the presented scheme improves the ride comfort even when the uncertain parameter exists. Due to the existence of uncertain terms, the NNs are used to approximate unknown functions in the ASSs. Finally, a simulation for a servo system with hydraulic actuator is shown to verify the effectiveness and reliability of the proposed approach.

In the novel, an adaptive neural network (NN) controller is developed for a category of nonlinear stochastic systems with full state constraints and unknown time delays. The control quality and system stability suffer from the problems of state time delays and constraints which frequently arises in most real plants. The considered systems are transformed into new constrained free systems based on nonlinear mappings, such that full state constraints are never violated and the feasibility conditions on virtual controllers (the values of virtual controllers and its derivative are assumed to be known) are removed. To compensate for unknown time delayed uncertainties, the exponential type Lyapunov-Krasovskii functionals (LKFs) are employed. NNs are utilized to approximate unknown nonlinear functions appearing in the design procedure. In addition, by employing dynamic surface control (DSC) technique and less adjustable parameters, the online computation burden is lightened. The control method presented can achieve the semiglobal uniform ultimate boundedness of all the closed-loop system signals and the satisfactions of full state constraints by rigorous proof. Finally, by presenting simulation examples, the efficiency of the presented approach is revealed.

This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper.

This paper investigates adaptive fuzzy output feedback fault-tolerant optimal control problem for a class of single-input and single-output nonlinear systems in strict feedback form. The considered nonlinear systems contain unknown nonaffine nonlinear faults and unmeasured states. Fuzzy logic systems are used to approximate cost function and unknown nonlinear functions, respectively. It is assumed that the states of the systems to be controlled are unmeasurable, thus an adaptive state observer is developed. To solve the nonaffine nonlinear fault control design problem, filtered signals are introduced into the adaptive backstepping control design procedures, and in the framework of adaptive critic technique and fault-tolerant control technique, a novel adaptive fuzzy fault-tolerant optimal control scheme is developed. The stability of the closed-loop system is proved by using Lyapunov stability theory. The simulation results verify the effectiveness of the proposed control strategy.

This paper concentrates upon the problem of finite-time fault-tolerant control for a class of switched nonlinear systems in lower-triangular form under arbitrary switching signals. Both loss of effectiveness and bias fault in actuator are taken into account. The method developed extends the traditional finite-time convergence from nonswitched lower-triangular nonlinear systems to switched version by designing appropriate controller and adaptive laws. In contrast to the previous results, it is the first time to handle the fault tolerant problem for switched system while the finite-time stability is also necessary. Meanwhile, there exist unknown internal dynamics in the switched system, which are identified by the radial basis function neural networks. It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability. Finally, an illustrative simulation on a resistor-capacitor-inductor circuit is proposed to further demonstrate the effectiveness of the theoretical result.

The adaptive fuzzy containment control problem is discussed for high-order systems with unknown nonlinear dynamics and unmeasurable states guided by multiple dynamic leaders. A high gain observer is introduced to reconstruct the system states. Then, utilizing fuzzy logic systems to model followers' dynamics, an observer-based adaptive fuzzy containment control approach is presented using only the relative position of the neighbors. It is shown that the uniformly ultimately bounded containment control is realized under the condition that, each follower can obtain the information from at least one leader through a directed path. As an extension, an observer-based containment control with prescribed performance is developed, which guarantees the relative position error to be bounded by a specified bound. The obtained theoretical results are validated by simulation examples.

This paper investigates the finite-time adaptive fuzzy control problem for a class of multi-input and multi-output (MIMO) nonlinear nonstrict feedback systems. During the control design process, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and fuzzy state observer is constructed to estimate the unmeasured states. By combining adaptive backstepping with the dynamic surface control (DSC) technique, a finite-time fuzzy adaptive control scheme is presented to overcome the “explosion of complexity” problem. The stability of the close-loop systems can be proved based on the finite-time Lyapunov stability theory. The presented control scheme demonstrates that the closed-loop systems are semiglobal practical finite-time stability, and tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to show the effectiveness of the presented control method.

In this paper, a framework of adaptive control for a switched nonlinear system with multiple prescribed performance bounds is established using an improved dwell time technique. Since the prescribed performance bounds for subsystems are different from each other, the different coordinate transformations have to be tackled when the system is transformed, which have not been encountered in some switched systems. We deal with the different coordinate transformations by finding a specific relationship between any two different coordinate transformations. To obtain a much less conservative result, in contrast to the common adaptive law, different adaptive laws are established for both active and inactive time-interval of each subsystem. The proposed controllers and switching signals guarantee that all signals appearing in the closed-loop system are bounded. Furthermore, both transient-state and steady-state performances of the switched system are obtained. Finally, the effectiveness of the developed method is verified by the application to a continuous stirred tank reactor system.

This paper solves the stochastically finite-time control problem for uncertain stochastic nonlinear systems in nontriangular form. The considered controlled plants are different from the previous results of finite-time control systems, which are the multiple-input and multiple-output (MIMO) stochastic systems with the unknown functions consisting of all states, stochastic disturbance, and immeasurable states. Fuzzy logic systems and a state filter are used to model the uncertain systems and estimate the immeasurable states, respectively. Based on the finite-time theory and Itȏ differential equation, a novel stochastically finite-time stability theorem is first raised. By combining the novel criterion and backstepping technique, an adaptive fuzzy stochastically finite-time control method is proposed. It is testified that all signals in the closed-loop signals are semiglobal finite-time stable in probability, and the tracking performances are well. Simulation example results further show the effectiveness of the proposed approach.

In this paper, the distributed adaptive fuzzy containment control problem is investigated for a class of uncertain nonlinear systems guided by multiple dynamic leaders. Each follower is modeled by nonlinear strict-feedback systems subject to full state constraints. The function approximation technique using fuzzy logic systems is utilized to identify the unknown nonlinearities of each follower. Both the state feedback containment control and the observer-based output feedback containment control are constructed by combining distributed sliding-mode estimators with adaptive fuzzy backstepping control. To prevent constraint violation, multiple barrier Lyapunov functions associated with error surfaces are introduced in the control design. It is proven that uniformly ultimately bounded containment control is achieved without violating full state constraints under the condition that for each follower, there exists at least one leader that has a directed path to that follower. Simulation studies are performed to show the effectiveness of the proposed theoretical results.

The adaptive fuzzy containment control problem is addressed for multiple uncertain nonlinear strict-feedback systems with immeasurable states and multiple leaders under directed communication graphs. By utilizing fuzzy logic systems to model the followers’ dynamics, a distributed fuzzy state observer is designed for the state estimation using only the relative position information. Then, an observer-based containment control scheme is constructed by the adaptive fuzzy control technique as well as the command filter. The filtering error loop is introduced to compensate the error arising from the command filter. The proposed adaptive fuzzy containment control scheme guarantees that all followers are driven into the dynamic convex hull spanned by the leaders with a bounded containment error, if there exists at least one of the leaders who has a directed path to the follower. Simulation results are given to illustrate the control performance of the proposed containment control method.

This paper proposes an adaptive neural control method for a class of nonlinear time-varying delayed systems with time-varying full-state constraints. To address the problems of the time-varying full-state constraints and time-varying delays in a unified framework, an adaptive neural control method is investigated for the first time. The problems of time delay and constraint are the main factors of limiting the system performance severely and even cause system instability. The effect of unknown time-varying delays is eliminated by using appropriate Lyapunov-Krasovskii functionals. In addition, the constant constraint is the only special case of time-varying constraint which leads to more complex and difficult tasks. To guarantee the full state always within the time-varying constrained interval, the time-varying asymmetric barrier Lyapunov function is employed. Finally, two simulation examples are given to confirm the effectiveness of the presented control scheme.

In this paper, an optimal control algorithm is designed for uncertain nonlinear systems in discrete-time, which are in nonaffine form and with unknown dead-zone. The main contributions of this paper are that an optimal control algorithm is for the first time framed in this paper for nonlinear systems with nonaffine dead-zone, and the adaptive parameter law for dead-zone is calculated by using the gradient rules. The mean value theory is employed to deal with the nonaffine dead-zone input and the implicit function theory based on reinforcement learning is appropriately introduced to find an unknown ideal controller which is approximated by using the action network. Other neural networks are taken as the critic networks to approximate the strategic utility functions. Based on the Lyapunov stability analysis theory, we can prove the stability of systems, i.e., the optimal control laws can guarantee that all the signals in the closed-loop system are bounded and the tracking errors are converged to a small compact set. Finally, two simulation examples demonstrate the effectiveness of the design algorithm.

This paper solves the finite-time switching control issue for the nonstrict-feedback nonlinear switched systems. The controlled plants contain immeasurable states, arbitrarily switchings, and the unknown functions which are constructed with the whole states. Neural network is used to simulate the uncertain systems and a filter-based state observer is designed to estimate the immeasurable states in this paper, respectively. Based on the backstepping recursive technique and the common Lyapunov function method, a finite-time switching control method is presented. Due to the developed finite-time control strategy, the closed-loop signals can be ensured to be bounded under arbitrarily switchings, and the outputs of systems can quickly track the desired reference signals in finite time. The effectiveness of the proposed method is given through its application to a mass-spring-damper system.

This paper studies the fuzzy adaptive distributed event-based control scheme for a class of uncertain nonlinear multiagent systems in strict feedback form. A novel distributed adaptive event-trigger condition and event-triggered controller are designed simultaneously. The main advantage with respect to event-sampling states is that the controllers were updated in an aperiodic manner at the event sampled instants, saving the computation resource and transmission load. Simulation results have shown satisfactory tracking performance of the developed control scheme.

This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.

This paper studies the adaptive fuzzy bounded control problem for leader-follower multiagent systems, where each follower is modeled by the uncertain nonlinear strict-feedback system. Combining the fuzzy approximation with the dynamic surface control, an adaptive fuzzy control scheme is developed to guarantee the output consensus of all agents under directed communication topologies. Different from the existing results, the bounds of the control inputs are known as a priori, and they can be determined by the feedback control gains. To realize smooth and fast learning, a predictor is introduced to estimate each error surface, and the corresponding predictor error is employed to learn the optimal fuzzy parameter vector. It is proved that the developed adaptive fuzzy control scheme guarantees the uniformly ultimate boundedness of the closed-loop systems, and the tracking error converges to a small neighborhood of the origin. The simulation results and comparisons are provided to show the validity of the control strategy presented in this paper.

In this paper, an adaptive fuzzy fault-tolerant control approach is proposed for a class of nontriangular structure nonlinear systems, which contain immeasurable states and unknown actuator faults (actuator loss-of-effectiveness and bias fault). It should be noted that if the existing approaches are employed for nontriangular structure nonlinear systems, the algebraic loop problem may occur. In this study, fuzzy logic systems are employed to approximate unknown nonlinear functions, and a fuzzy state observer is designed to estimate immeasurable states. Then, based on the property of performance function and simple barrier Lyapunov function design method, the prescribed output tracking error dynamic performance and the corresponding stability are guaranteed. By using the parameter estimation technique, a new fault compensation strategy is developed to relax the requirement that the efficiency indicator must be known. The stability of the closed-loop system is proved by using the Lyapunov function stability theory. Finally, a simulation example is given to validate the effectiveness of the proposed control strategy.

The problem of adaptive fuzzy decentralized fault-tolerant optimal control is investigated for nonlinear large-scale systems with actuator faults in this paper. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions and learn cost functions. Filtered signals are adopted to circumvent the problems of an algebraic loop on designing the decentralized controllers. Based on the backstepping technique and fault-tolerant control technique, a decentralized feedforward control strategy is designed. Based on the adaptive critic technique, a decentralized feedback optimal control strategy is designed. By combining the feedforward control strategy with the feedback optimal control strategy, a novel adaptive fuzzy decentralized fault-tolerant optimal control scheme is established. The stability of the closed-loop system is proved by using the Lyapunov stability theory. The effectiveness of the proposed decentralized control approach is confirmed via a simulation example.

In this paper, an adaptive fuzzy control method with prescribed performance is proposed for multi-input and multioutput block-triangular-structured nonlinear systems with immeasurable states. Fuzzy logic systems are adopted to identify the unknown nonlinear system functions. Adaptive fuzzy state observers are designed to solve the problem of unmeasured states, and a new observer-based output-feedback control scheme is developed based on adaptive fuzzy control principle and bacsktepping design technique. The proposed control method not only overcomes the problem of “explosion of complexity” existing in the backstepping design, but also removes the restrictive assumption that unknown nonlinear functions must satisfy global Lipschitz condition. The proposed scheme can ensure that all variables of the control systems are semiglobally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. Simulation results of chemical process control system are presented to further demonstrate the effectiveness of the proposed control strategy.

In the paper, the adaptive observer and controller designs based fuzzy approximation are studied for a class of uncertain nonlinear systems in strict feedback. The main properties of the considered systems are that all the state variables are not available for measurement and at the same time, they are required to limit in each constraint set. Due to the properties of systems, it will be a difficult task for designing the controller and the stability analysis. Based on the structure of the considered systems, a fuzzy state observer is framed to estimate the unmeasured states. To ensure that all the states do not violate their constraint bounds, the Barrier type of functions will be employed in the controller and the adaptation laws. In the stability analysis, the effect caused by the constraints for all the states can be overcome by using the Barrier Lyapunov functions. Based on the proposed control approach, it is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example.

This paper solves the finite-time decentralized control problem for uncertain nonlinear large-scale systems in nonstrict-feedback form. The considered controlled plants are different from the previous results of finite-time control systems, which are the nonstrict-feedback large-scale systems with the unknown functions consisting of all states, interactions, and immeasurable states. Fuzzy logic systems and a filter-based state observer are utilized to model uncertain systems and deal with the immeasurable states, respectively. By combining the backstepping recursive design with Lyapunov function theory, a finite-time adaptive fuzzy decentralized control approach is raised. It is testified that the developed control strategy can guarantee that the closed-loop signals are bounded, and the outputs of systems have satisfactory tracking performance in a finite time. A quadruple-tank process system is given to testify the effectiveness and applicability of the proposed approach.

In this paper, the problem of adaptive fuzzy decentralized optimal control is investigated for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinear functions and unmeasured states. By utilizing the fuzzy logic systems to approximate the unknown nonlinear functions and cost functions, a fuzzy state observer is established to estimate the unmeasured states. The control design is divided into two phases. First, by using the state observer and the backstepping design technique, a feedforward decentralized controller with parameters adaptive laws is designed, by which the original controlled strict-feedback nonlinear large-scale system is transformed into an equivalent affine nonlinear large-scale system. Second, by using adaptive dynamic programming theory, a feedback decentralized optimal controller is developed for the equivalent affine nonlinear system. The whole adaptive fuzzy decentralized optimal control scheme consists of a feedforward decentralized controller and a feedback decentralized optimal controller. It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero. In addition, the proposed control approach can guarantee that the cost functions are minimized. Simulation results are given to demonstrate the effectiveness of the proposed control approach.

In this paper, an adaptive neural net- works (NNs)-based decentralized control scheme with the prescribed performance is proposed for uncertain switched nonstrict-feedback interconnected nonlinear systems. It is assumed that nonlinear interconnected terms and nonlinear functions of the concerned systems are unknown, and also the switching signals are unknown and arbitrary. A linear state estimator is constructed to solve the problem of unmeasured states. The NNs are employed to approximate unknown interconnected terms and nonlinear functions. A new output feedback decentralized control scheme is developed by using the adaptive backstepping design technique. The control design problem of nonlinear interconnected switched systems with unknown switching signals can be solved by the proposed scheme, and only a tuning parameter is needed for each subsystem. The proposed scheme can ensure that all variables of the control systems are semi-globally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by some simulation results.

The decentralized adaptive fuzzy control problem for switched nonstrict-feedback nonlinear large-scale systems is investigated in this paper. Fuzzy logic systems are adopted to identify the unknown nonlinear system functions and unknown interconnected nonlinearities. A linear state observer is designed to solve the problem of unmeasured states, and a new observer-based output-feedback decentralized control scheme is developed based on adaptive fuzzy control principle and bacsktepping design technique. The proposed control strategy not only solves the control design problem of more general form nonlinear switched systems in nonstrict-feedback form, but also does not require the switched signals to meet the restriction of average dwell time. The stability of fuzzy control systems under arbitrary switchings is proven based on the common Lyapunov function method. Simulation results of numerical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

This paper deals with the tracking control problem for a class of nonlinear multiple input multiple output unknown time-varying delay systems with full state constraints. To overcome the challenges which cause by the appearances of the unknown time-varying delays and full-state constraints simultaneously in the systems, an adaptive control method is presented for such systems for the first time. The appropriate Lyapunov-Krasovskii functions and a separation technique are employed to eliminate the effect of unknown time-varying delays. The barrier Lyapunov functions are employed to prevent the violation of the full state constraints. The singular problems are dealt with by introducing the signal function. Finally, it is proven that the proposed method can both guarantee the good tracking performance of the systems output, all states are remained in the constrained interval and all the closed-loop signals are bounded in the design process based on choosing appropriate design parameters. The practicability of the proposed control technique is demonstrated by a simulation study in this paper.

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

This paper proposes an fuzzy adaptive output-feedback stabilization control method for nonstrict feedback uncertain switched nonlinear systems. The controlled system contains unmeasured states and unknown nonlinearities. First, a switched state observer is constructed in order to estimate the unmeasured states. Second, a variable separation approach is introduced to solve the problem of nonstrict feedback. Third, fuzzy logic systems are utilized to identify the unknown uncertainties, and an adaptive fuzzy output feedback stabilization controller is set up by exploiting the backstepping design principle. At last, by applying the average dwell time method and Lyapunov stability theory, it is proven that all the signals in the closed-loop switched system are bounded, and the system output converges to a small neighborhood of the origin. Two examples are given to further show the effectiveness of the proposed switched control approach.

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

A neural network (NN) adaptive control design problem is addressed for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. The considered systems contain uncertainty dynamics and their states are enforced to subject to bounded constraints as well as the couplings among various inputs and outputs are inserted in each subsystem. To stabilize this class of systems, a novel adaptive control strategy is constructively framed by using the backstepping design technique and NNs. The novel integral barrier Lyapunov functionals (BLFs) are employed to overcome the violation of the full state constraints. The proposed strategy can not only guarantee the boundedness of the closed-loop system and the outputs are driven to follow the reference signals, but also can ensure all the states to remain in the predefined compact sets. Moreover, the transformed constraints on the errors are used in the previous BLF, and accordingly it is required to determine clearly the bounds of the virtual controllers. Thus, it can relax the conservative limitations in the traditional BLF-based controls for the full state constraints. This conservatism can be solved in this paper and it is for the first time to control this class of MIMO systems with the full state constraints. The performance of the proposed control strategy can be verified through a simulation example.

This paper investigates a robust adaptive fuzzy control stabilization problem for a class of uncertain nonlinear systems with arbitrary switching signals that use an observer-based output feedback scheme. The considered switched nonlinear systems possess the unstructured uncertainties, unmodeled dynamics, and without requiring the states being available for measurement. A state observer which is independent of switching signals is designed to solve the problem of unmeasured states. Fuzzy logic systems are used to identify unknown lumped nonlinear functions so that the problem of unstructured uncertainties can be solved. By combining adaptive backstepping design principle and small-gain approach, a novel robust adaptive fuzzy output feedback stabilization control approach is developed. The stability of the closed-loop system is proved via the common Lyapunov function theory and small-gain theorem. Finally, the simulation results are given to demonstrate the validity and performance of the proposed control strategy.

This paper investigates an output-feedback control design problem for a class of switched continuous-time Takagi-Sugeno (T-S) fuzzy systems. The considered fuzzy systems consist of several switching modes and each switching mode is described by T-S fuzzy models. In addition, there exists the asynchronous switching between the system switching modes and the controller switching modes. By using parallel distributed compensation design method, the output-feedback control schemes are developed based on state observers for the measurable and immeasurable premise variables cases. The sufficient conditions of ensuring the switched control system stabilization are proposed based on the theory of Lyapunov stability and average-dwell time methods. The controller and observer gains are obtained via two-step method. An illustrated numerical example is provided to show the effectiveness of the proposed control approaches.

The adaptive fuzzy tracking control design problem for multi-input and multi-output uncertain switched nonstrict-feedback nonlinear systems with arbitrary switchings is investigated in this paper. Fuzzy logic systems are introduced to identify the unknown nonlinear functions (for state measurable case) and model the uncertain nonlinear systems (for state immeasurable case). Both state feedback and observer-based output feedback control design schemes are developed based on combined command filter and adaptive fuzzy control technique. The proposed adaptive fuzzy controllers not only solve the “explosion of complexity” problem existing in conventional backstepping control schemes, but as well as avoid the calculation of partial derivatives. Furthermore, the stability of the fuzzy control systems under arbitrary switchings is proven based on the common Lyapunov function method. Two simulation examples are presented to further demonstrate the effectiveness of the proposed control strategies.

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

In this paper, an adaptive control approach-based neural approximation is developed for a class of uncertain nonlinear discrete-time (DT) systems. The main characteristic of the considered systems is that they can be viewed as a class of multi-input multioutput systems in the nonstrict feedback structure. The similar control problem of this class of systems has been addressed in the past, but it focused on the continuous-time systems. Due to the complicacies of the system structure, it will become more difficult for the controller design and the stability analysis. To stabilize this class of systems, a new recursive procedure is developed, and the effect caused by the noncausal problem in the nonstrict feedback DT structure can be solved using a semirecurrent neural approximation. Based on the Lyapunov difference approach, it is proved that all the signals of the closed-loop system are semiglobal, ultimately uniformly bounded, and a good tracking performance can be guaranteed. The feasibility of the proposed controllers can be validated by setting a simulation example.

In this paper, we address an adaptive control problem for a class of nonlinear strict-feedback systems with uncertain parameter. The full states of the systems are constrained in the bounded sets and the boundaries of sets are compelled in the asymmetric time-varying regions, i.e., the full state time-varying constraints are considered here. This is for the first time to control such a class of systems. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and we also establish a novel control TABLF scheme to ensure the asymptotic output tracking performance. The performances of the adaptive TABLF-based control are verified by a simulation example.

An adaptive control-based neural network for a n-link robot is studied and the considered robot can be transformed as a class of multi-input-multioutput systems. The position of the robot or the output of the transformed systems is constrained in a time-varying compact set. It is commonly known that the constant constraint belongs to a special case of the time-varying constraint, and thus, it can be more general for handling practical problem as compared with the existing methods for robot. The neural approximation is used to estimate the unknown functions of systems and the time-varying barrier Lyapunov function is used to overcome the violation of constraints. It can prove the stability of the closed-loop systems by using Lyapunov analysis. The feasibility of the approach is demonstrated by performing a simulation example.

This paper investigates fuzzy adaptive output feedback optimal control problem for a class of strict-feedback nonlinear systems. With the help of fuzzy logic systems approximating the unknown nonlinear functions and cost function, the unmeasured states are estimated by designing fuzzy adaptive state observer. Combining state observer with backstepping design technique, a feedforward controller is designed. Based on the designed feedforward control strategy, the controlled nonlinear system can be converted to an equivalence nonlinear system in affine-form. Finally, a fuzzy adaptive optimal controller with parameters adaptive laws is developed. The whole control scheme consists of a feedforward controller and a feedback optimal controller. It is shown that the proposed output feedback optimal control approach can guarantee that all signals in the closed-loop system are bounded, and the system output can track the reference signal. In addition, the proposed control approach can guarantee cost function is the smallest. Simulation results are given to demonstrate the effectiveness of the proposed control approach.

In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown nonlinear discrete-time systems. The controlled systems are in a block-triangular multi-input-multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.

This paper studies an adaptive neural control for nonlinear multiple-input multiple-output systems in interconnected form. The studied systems are composed of N subsystems in pure feedback structure and the interconnection terms are contained in every equation of each subsystem. Moreover, the studied systems consider the effects of Prandtl-Ishlinskii (PI) hysteresis model. It is for the first time to study the control problem for such a class of systems. In addition, the proposed scheme removes an important assumption imposed on the previous works that the bounds of the parameters in PI hysteresis are known. The radial basis functions neural networks are employed to approximate unknown functions. The adaptation laws and the controllers are designed by employing the backstepping technique. The closed-loop system can be proven to be stable by using Lyapunov theorem. A simulation example is studied to validate the effectiveness of the scheme.

In this paper, a hybrid fuzzy adaptive output feedback control design approach is proposed for a class of multiinput and multioutput strict-feedback nonlinear systems with unknown time-varying delays, unmeasured states, and input saturation. First, fuzzy logic systems are employed to approximate unknown nonlinear functions in the system. Next, a smooth function is used to approximate the input saturation and an adaptive fuzzy state observer is constructed to solve the problem of unmeasured states. Based on the designed adaptive fuzzy state observer, a serial-parallel estimation model is established. By applying adaptive fuzzy dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws is developed based on Lyapunov-Krasovskii functional. It is proved that all variables of the closed-loop system are bounded and the system outputs can follow the given bounded reference signals as close as possible. A simulation example is provided to further show the effectiveness of this novel control scheme.

In this paper, an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete-time systems. The controlled systems are in a strict-feedback frame and contain unknown functions and nonsymmetric dead-zone. For this class of systems, the control objective is to design a controller, which not only guarantees the stability of the systems, but achieves the optimal control performance as well. This immediately brings about the difficulties in the controller design. To this end, the fuzzy logic systems are employed to approximate the unknown functions in the systems. Based on the utility functions and the critic designs, and by applying the backsteppping design technique, a reinforcement learning algorithm is used to develop an optimal control signal. The adaptation auxiliary signal for unknown dead-zone parameters is established to compensate for the effect of nonsymmetric dead-zone on the control performance, and the updating laws are obtained based on the gradient descent rule. The stability of the control systems can be proved based on the difference Lyapunov function method. The feasibility of the proposed control approach is further demonstrated via two simulation examples.

In this paper, an adaptive fuzzy controller is constructed for a class of nonlinear discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain nonlinear discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples.

This paper studies adaptive fuzzy output feedback tracking control problem for nonstrict-feedback switched nonlinear systems. The switched systems under consideration contain unknown nonlinearities, unmeasured states, and unknown deadzones. Fuzzy logic systems are utilized to approximate the unknown nonlinearities, and a switched fuzzy state observer is designed, and thus, the immeasurable states are estimated via it. In the framework of observer-based output feedback control, and by using the certainty equivalence deadzone inverse, a novel adaptive fuzzy output feedback control design method with the parameters adaptation laws is developed. The stability of the closed-loop system and the convergence of the tracking error are proved based on Lyapunov function and the average dwell-time methods. Two simulation examples are provided to check the effectiveness of the proposed approach.

This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.

In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.

This paper discusses the adaptive fuzzy partial tracking errors constrained control problem for a class of uncertain stochastic nonlinear systems. The concerned systems contain the unknown nonlinear functions, unmeasured state variables, and the switching signal with average dwell time. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and a switched fuzzy state observer is developed for estimating the unmeasured states. By introducing the performance function and error transformation into the backstepping dynamic surface control design, a new observer-based adaptive fuzzy control design approach is developed. By employing the multiple Lyapunov function and the average dwell time methods, it is proved that all the signals of the resulting closed-loop system are bounded, and the partial tracking errors are confined all times within the prescribed bounds. A simulation example is provided to show the effectiveness of the proposed approach.

In this paper, the problem of adaptive fuzzy decentralized output-feedback control design is investigated for a class of switched nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinearities and dead zones, the switching signals with average dwell time, and without the direct requirement of the states being available for feedback. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a fuzzy switched decentralized state observer is designed and thus via it the immeasurable states are obtained. By applying the adaptive decentralized backstepping design technique, an adaptive fuzzy decentralized output-feedback tracking control approach is developed for the switched subsystems. The stability of the whole closed-loop system is proved by using the Lyapunov function and the average dwell-time methods. Satisfactory tracking performance is achieved under the switching signals with average dwell time. The simulation example is provided to indicate the effectiveness of the proposed control method.

In this paper, an adaptive fuzzy decentralized output feedback control design is presented for a class of interconnected nonlinear pure-feedback systems. The considered nonlinear systems contain unknown nonlinear uncertainties and the states are not necessary to be measured directly. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed and the estimations of the immeasurable state variables are obtained. Based on the adaptive backstepping dynamic surface control design technique, an adaptive fuzzy decentralized output feedback control scheme is developed. It is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and also that the observer and tracking errors are guaranteed to converge to a small neighborhood of the origin. Some simulation results and comparisons with the existing results are provided to illustrate the effectiveness and merits of the proposed approach.

In this paper, a composite adaptive fuzzy output-feedback control approach is proposed for a class of single-input and single-output strict-feedback nonlinear systems with unmeasured states and input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws are developed. It is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with previous control methods are provided to show the effectiveness of the proposed approach.

In the paper, an adaptive tracking control design is studied for a class of nonlinear discrete-time systems with dead-zone input. The considered systems are of the nonaffine pure-feedback form and the dead-zone input appears nonlinearly in the systems. The contributions of the paper are that: 1) it is for the first time to investigate the control problem for this class of discrete-time systems with dead-zone; 2) there are major difficulties for stabilizing such systems and in order to overcome the difficulties, the systems are transformed into an n-step-ahead predictor but nonaffine function is still existent; and 3) an adaptive compensative term is constructed to compensate for the parameters of the dead-zone. The neural networks are used to approximate the unknown functions in the transformed systems. Based on the Lyapunov theory, it is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of zero. Two simulation examples are provided to verify the effectiveness of the control approach in the paper.

In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach.

In this paper, an adaptive fuzzy backstepping output-feedback tracking control approach is proposed for a class of multi-input and multi-output (MIMO) stochastic nonlinear systems. The MIMO stochastic nonlinear systems under study are assumed to possess unstructured uncertainties, unknown dead-zones, and unknown control directions. By using a linear state transformation, the unknown control coefficients and the unknown slopes characteristic of the dead-zones are lumped together, and the original system is transformed to a new system on which the control design becomes feasible. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By introducing a special Nussbaum gain function into the backstepping control design, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The main features of the proposed adaptive control approach are that it can guarantee the stability of the closed-loop system, and the tracking errors converge to a small neighborhood of zero. Moreover, it can solve the problems of unknown control direction, unknown dead-zone, and unmeasured states simultaneously. Two simulation examples are provided to show the effectiveness of the proposed approach.

The adaptive fuzzy identification and control problems are considered for a class of multi-input multi-output nonlinear systems with unknown functions and unknown dead-zone inputs. The main characteristics of the considered systems are that 1) they are composed of n subsystems and each subsystem is in nested lower triangular form, 2) dead-zone inputs are in nonsymmetric nonlinear form, and 3) dead-zone inputs appear nonlinearly in the systems and their parameters are not required to be known. The controller design for this class of systems is a difficult and complicated task because of the existences of unknown functions, the couplings among the nested subsystems, and the dead-zone inputs. In the controller design, the fuzzy logic systems are employed to approximate the unknown functions and the differential mean value theorem is used to separate dead-zone inputs. To compensate for dead-zone inputs, the compensative terms are designed in the controllers. The stability of the closed-loop system is proved via the Lyapunov stability theorem. A simulation example is provided to validate the feasibility of the approach.

In this paper, a partial tracking error constrained fuzzy output-feedback dynamic surface control (DSC) scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems. The considered MIMO nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design. With the help of fuzzy logic systems identifying the MIMO unknown nonlinear systems, a fuzzy adaptive observer is established to estimate the unmeasured states. By transforming the tracking errors into new virtual error variables and based on the DSC backstepping recursive design technique, a new adaptive fuzzy output-feedback control method is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds. The simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme.

This paper is concerned with the problem of type-2 fuzzy adaptive inverse control for a cable-driven parallel system. Based on the heuristics and prior knowledge of the system, the system is divided into six subsystems. The proposed control scheme for each subsystem contains a forward model and a fuzzy adaptive inverse controller (FAIC), which are expressed by an interval type-2 fuzzy nonlinear autoregressive exogenous (NARX) model, respectively. To construct the antecedents of the interval type-2 fuzzy NARX forward models and FAICs, the monotonic property of the fuzzy NARX model is first proved, and then, their antecedent parameters can be determined by this property. Furthermore, the consequent parameters of the forward models are computed offline via a constrained least squares algorithm, and the consequent parameters of the FAIC are adjusted online via a recursive least squares algorithm. Experiment results are provided to show that the proposed type-2 fuzzy control scheme can realize the control objectives and achieve a good control performance.

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

In this paper, the problem of fuzzy adaptive state-feedback control is investigated for a class of switched uncertain nonlinear large-scale systems. There exist switching jumps and uncertainties in systems models and switching signals, respectively. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and combining the adaptive backstepping technique and the dwell-time property of the switching signal, an adaptive fuzzy state-feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of the origin.

This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

In this paper, an adaptive fuzzy output-feedback control is investigated for a class of pure-feedback uncertain nonlinear systems with unknown dead-zone inputs and immeasurable states. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, and a state filter observer is designed to estimate the unmeasured states. Based on the information of the dead-zone slopes as well as treating the unknown inputs coefficients as a system uncertainty, a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique. The stability of the resulting closed-loop system is proved and a simulation example is provided to show the effectiveness of the proposed control approach. The important feature of the proposed adaptive fuzzy controller is that it can solve the states immeasurable and the unknown dead-zone problems that exist in the previous publications and extends the existing results on strict-feedback control to the counterpart on pure-feedback control.

In this paper, an adaptive fuzzy robust output feedback control problem is considered for a class of single-input and single-output nonlinear systems in a strict-feedback form. The considered systems possess the unstructured uncertainties, unknown dead zone, and the dynamics uncertainties, and they do not assume the states being available for the controller design. In the controller design, fuzzy logic systems are first used to approximate the unstructured uncertainties, and by utilizing the information of the bounds of the dead-zone slopes and treating the time-varying inputs coefficients as a system uncertainty, a fuzzy state observer is designed to estimate the unmeasured states. By combining a backstepping technique with a nonlinear small-gain approach, a new adaptive fuzzy robust output feedback control has been developed. It is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed-loop systems. Simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach.

An adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper. The considered systems are of the discrete-time form in a triangular structure and include the backlash and the external disturbance. By using the prediction function of future states, the systems are transformed into an n-step ahead predictor. The fuzzy logic systems (FLSs) are used to approximate the unknown functions, unknown backlash, and backlash inversion, respectively. A discrete-time tuning algorithm is developed to estimate the optimal fuzzy parameters. Compared with the previous works for the discrete-time systems with backlash, the main contributions of the paper are that 1) the rigorous restriction for the functional estimation error is removed, and 2) the external disturbance is bounded, but the bound is not required to be known. A novel controller and the adaptation laws are constructed by using the discrete Taylor series expansion and the difference Lyapunov analysis, and thus, those limitations in the previous works are overcome. It is proven that all the signals in the closed-loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set. A simulation example is provided to illustrate the effectiveness of the proposed approach.

This paper investigates the adaptive fuzzy decentralized fault-tolerant control (FTC) problem for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear system contains the unknown nonlinear functions, i.e., unmeasured states and actuator faults, which are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is designed to estimate the unmeasured states. By combining the backstepping technique with the nonlinear FTC theory, a novel adaptive fuzzy decentralized FTC scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded, and the tracking errors between the system outputs and the reference signals converge to a small neighborhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.

In this paper, an adaptive decentralized fuzzy output feedback stabilization problem is investigated for a class of uncertain stochastic nonlinear large-scale systems. The addressed stochastic nonlinear systems contain unknown nonlinear functions, unknown control direction, and without the measurements of the states. Fuzzy logic systems are used to identify the unknown nonlinear functions, and a fuzzy state filter observer is designed to estimate the unmeasured states. To solve the problem of the unknown control direction in decentralized control design, Nussbaum-type functions are introduced and new property on Nussbaum-type function is proved. Based on the backstepping recursive design technique and the established Nussbaum function property, a new robust stabilization control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded in probability, and the observer errors and system output converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approach.

This paper investigates fuzzy adaptive actuator failure compensation control for a class of uncertain stochastic nonlinear systems in strict-feedback form. These stochastic nonlinear systems contain the actuator faults of both loss of effectiveness and lock-in-place, unmodeled dynamics, and without direct measurements of state variables. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is established to estimate the unmeasured states. By introducing the dynamical signal and the changing supply function technique design into the backstepping control design, a robust adaptive fuzzy fault-tolerant control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are bounded in probability in the presence of the actuator failures and the unmodeled dynamics. Simulation results are provided to show the effectiveness of the control approach.

In this paper, the problems of stability and tracking control for a class of large-scale nonlinear systems with unmodeled dynamics are addressed by designing the decentralized adaptive fuzzy output feedback approach. Because the dynamic surface control technique is introduced, the designed controllers can avoid the issue of “explosion of complexity,” which comes from the traditional backstepping design procedure that deals with large-scale nonlinear systems with unmodeled dynamics. In addition, a reduced-order observer is designed to estimate those immeasurable states. Based on the Lyapunov stability method, it is proven that all the signals in the closed-loop system are bounded, and the system outputs track the reference signals to a small neighborhood of the origin by choosing the design parameters appropriately. The simulation examples are given to verify the effectiveness of the proposed techniques.

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi-input and multi-output (MIMO) strict-feedback nonlinear systems with both unknown nonsymmetric dead-zone inputs and immeasurable states. In this research, fuzzy logic systems are utilized to evaluate the unknown nonlinear functions, and a fuzzy adaptive state observer is established to estimate the unmeasured states. Based on the information of the bounds of the dead-zone slopes as well as treating the time-varying inputs coefficients as a system uncertainty, a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique. It is shown that the proposed control approach can assure that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded. It is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

In this paper, the problem of adaptive fuzzy decentralized backstepping control is considered for a class of nonlinear large-scale strict-feedback systems with unknown dead zones and immeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a state filter is designed to estimate the immeasurable states. Applying an adaptive backstepping design technique and combining it with the dead-zone inverse method, an adaptive fuzzy decentralized output-feedback backstepping control is developed. It is proved that all the signals of the resulting closed-loop adaptive control system are semiglobally uniformly ultimately bounded, and tracking errors converge to a small neighborhood of the origin by appropriate choice of design parameters. Simulation results are given to demonstrate that the proposed adaptive decentralized control approach has a satisfactory control performance.

In this paper, an adaptive fuzzy output feedback control approach is investigated for a class of stochastic nonlinear strict-feedback systems without the requirement of states measurement. The stochastic nonlinear system addressed in this paper is assumed to possess unstructured uncertainties (unknown nonlinear functions) and, in the presence of unmodeled dynamics, dynamics disturbances. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a fuzzy state observer is designed to estimate the unmeasured states. By combining the backstepping design technique with the stochastic small-gain approach, a new adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that the closed-loop system is input-state-practically stability (ISpS) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. Simulation results are included to indicate that the proposed adaptive fuzzy control approach has a satisfactory control performance. In addition, the simulation comparisons with the previous methods show that the proposed adaptive fuzzy control approach has robustness to the dynamical uncertainties.

In this paper, a novel adaptive fuzzy output feedback control scheme is presented for a class of SISO uncertain nonlinear systems in the presence of input saturation. The control design is achieved by combining adaptive fuzzy K-filter observer technique and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of fuzzy adaptive parameters is reduced to one, and three problems of “computational explosion”, “dimension curse”, “unmeasured states” are solved. A numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.

In this paper, an adaptive fuzzy backstepping control approach is considered for a class of nonlinear strict-feedback systems with unknown functions, unknown dead zones, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy filters state observer is designed to estimate the immeasurable states. By using the adaptive backstepping recursive design technique and constructing the dead-zone inverse, a new adaptive fuzzy backstepping output-feedback control approach is developed. It is mathematically proved that all the signals of the resulting closed-loop adaptive control system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin by appropriate choice of design parameters. The proposed approach cannot only solve the problem of the dead zones but also cancel the restrictive assumption in the previous literature that the states are all available for measurement. Two simulation examples are provided to show the effectiveness of the proposed approach.

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of uncertain multiple-input-multiple-output (MIMO) pure-feedback nonlinear systems with immeasurable states. The dynamic output feedback strategy begins with a state observer. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions. The filtered signals are introduced to circumvent algebraic loop problem encountered in the implementation of the controller, and an adaptive fuzzy output feedback is obtained via a backstepping recursive design technique. It is shown that the proposed control law can guarantee that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded and that the observer and tracking errors converge to a small neighborhood of the origin. Simulation studies are included to illustrate the effectiveness and potentials of the proposed techniques.

This brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi-input-multi-output (MIMO) systems in the discrete-time form. The considered MIMO systems are composed of n subsystems with the couplings of inputs and states among subsystems. In order to solve the noncausal problem and decouple the couplings, it needs to transform the systems into a predictor form. The higher order neural networks are utilized to approximate the desired controllers. By using Lyapunov analysis, it is proven that all the signals in the closed-loop system is the semi-globally uniformly ultimately bounded and the output errors converge to a compact set. In contrast to the existing results, the advantage of the scheme is that the number of the adjustable parameters is highly reduced. The effectiveness of the scheme is verified by a simulation example.

An adaptive output feedback control is studied for uncertain nonlinear single-input-single-output systems with partial unmeasured states. In the scheme, a reduced-order observer (ROO) is designed to estimate those unmeasured states. By employing radial basis function neural networks and incorporating the ROO into a new backstepping design, an adaptive output feedback controller is constructively developed. A prominent advantage is its ability to balance the control action between the state feedback and the output feedback. In addition, the scheme can be still implemented when all the states are not available. The stability of the closed-loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to validate the effectiveness of the proposed scheme.

In this paper, two adaptive neural network (NN) decentralized output feedback control approaches are proposed for a class of uncertain nonlinear large-scale systems with immeasurable states and unknown time delays. Using NNs to approximate the unknown nonlinear functions, an NN state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique with decentralized control design principle, an adaptive NN decentralized output feedback control approach is developed. In order to overcome the problem of "explosion of complexity" inherent in the proposed control approach, the dynamic surface control (DSC) technique is introduced into the first adaptive NN decentralized control scheme, and a simplified adaptive NN decentralized output feedback DSC approach is developed. It is proved that the two proposed control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the observer errors and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approaches.

In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of multiple-input-multiple-output nonlinear systems with immeasurable states. Using fuzzy-logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive-backstepping technique and DSC technique, an adaptive fuzzy output-feedback backstepping-control approach is developed. The proposed control method not only overcomes the problem of "explosion of complexity" inherent in the backstepping-design methods but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed-loop adaptive-control system are semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

In this paper, two adaptive fuzzy output feedback control approaches are proposed for a class of uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the fuzzy state observer, and by combining the adaptive backstepping technique with fuzzy adaptive control design, an adaptive fuzzy output feedback control approach is developed. To overcome the problem of "explosion of complexity" inherent in the proposed control method, the dynamic surface control (DSC) technique is incorporated into the first adaptive fuzzy control scheme, and a simplified adaptive fuzzy output feedback DSC approach is developed. It is proved that these two control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and the observer errors and the output of the system converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approaches.

In this paper, an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large-scale strict-feedback nonlinear systems without the measurements of the states. The nonlinear systems in this paper are assumed to possess unstructured uncertainties, time-varying delays, and unknown high-frequency gain sign. Fuzzy logic systems are used to approximate the unstructured uncertainties, K-filters are designed to estimate the unmeasured states, and a special Nussbaum gain function is introduced to solve the problem of unknown high-frequency gain sign. Combining the backstepping technique with adaptive fuzzy control theory, an adaptive fuzzy decentralized robust output feedback control scheme is developed. In order to obtain the stability of the closed-loop system, a new lemma is given and proved. Based on this lemma and Lyapunov-Krasovskii functions, it is proved that all the signals in the closed-loop system are uniformly ultimately bounded and that the tracking errors can converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated from simulation results.

This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

Robust adaptive-fuzzy-tracking control of a class of uncertain multi-input/multi-output nonlinear systems with coupled interconnections is considered in this paper. Takagi–Sugeno (T–S) fuzzy systems are used to approximate the unknown system functions. A novel adaptive-control scheme is developed on the basis of the so-called “dynamic-surface control” and “minimal-learning parameters” techniques. The proposed scheme has following two key features. First, the number of parameters updated online for each subsystem is reduced to one, and both problems of “curse of dimension” for high-dimensional systems and “explosion of complexity” inherent in the conventional backstepping methods are circumvented. Second, the potential controller-singularity problem in some of the existing adaptive-control schemes with feedback-linearization techniques is overcome. It is shown via Lyapunov theory that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. Finally, simulation results via two examples are presented to demonstrate the effectiveness and advantages of the proposed scheme.

In this paper, an adaptive fuzzy-decentralized robust output-feedback-control approach is proposed for a class of large-scale strict-feedback nonlinear systems with the unmeasured states. The large-scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties, unmodeled dynamics, and unknown high-frequency-gain sign. Fuzzy-logic systems are used to approximate the unstructured uncertainties, K-filters are designed to estimate the unmeasured states, and a dynamical signal and a special Nussbaum gain function are introduced into the control design to solve the problem of unknown high-frequency-gain sign and dominate unmodeled uncertainties, respectively. Based on the backstepping design and adaptive fuzzy-control methods, an adaptive fuzzy-decentralized robust output-feedback-control scheme is developed. It is proved that the proposed adaptive fuzzy-control approach can guarantee that all the signals in the closed-loop system are uniformly and ultimately bounded, and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by using simulation results.

A robust adaptive tracking control approach is presented for a class of strict-feedback single-input-single-output nonlinear systems. By employing radial-basis-function neural networks to account for system uncertainties, the proposed scheme is developed by combining "dynamic surface control" and "minimal learning parameter" techniques. The key features of the algorithm are that, first, the problem of "explosion of complexity" inherent in the conventional backstepping method is avoided, second, the number of parameters updated online for each subsystem is reduced to 2, and, third, the possible controller singularity problem in the approximation-based adaptive control schemes with feedback linearization technique is removed. These features result in a much simpler adaptive control algorithm, which is convenient to implement in applications. In addition, it is shown via input-to-state stability theory and small gain approach that all signals in the closed-loop system are semiglobal uniformly ultimately bounded. Finally, three simulation examples are used to demonstrate the effectiveness of the proposed scheme.

A robust adaptive fuzzy control approach is developed for a class of multi-input-multi-output (MIMO) nonlinear systems with modeling uncertainties and external disturbances by using both the approximation property of the fuzzy logic systems and the backstepping technique. The MIMO systems are composed of interconnected subsystems in the strict-feedback form. The main characteristics of the developed approach are that the online computation burden is alleviated and the robustness to dynamic uncertainties and external disturbances is improved. It is proven that all the signals of the resulting closed-loop system are uniformly bounded and that the tracking errors converge to a small neighborhood around zero. Two simulation experiments are presented to demonstrate the feasibility of the approach developed in this paper.

In this paper, an adaptive fuzzy output feedback control approach is proposed for single-input-single-output nonlinear systems without the measurements of the states. The nonlinear systems addressed in this paper are assumed to possess unmodeled dynamics in the presence of unstructured uncertainties and dynamic disturbances, where the unstructured uncertainties are not linearly parameterized, and no prior knowledge of their bounds are available. Fuzzy logic systems are used to approximate the unstructured uncertainties, and a state observer is developed to estimate the unmeasured states. By combining the backstepping technique with the small-gain approach, a stable adaptive fuzzy output feedback control method is proposed. It is shown that by applying the proposed adaptive fuzzy control approach, the closed-loop systems are semiglobally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated from simulation results.

This paper discusses the stabilization of Takagi-Sugeno (T-S) fuzzy systems with bounded and time-varying input delay. The robust stabilization via state feedback is first addressed, and delay-dependent stabilization conditions are proposed in terms of LMIs. Observer-based feedback stabilization is also discussed for T-S fuzzy input delay systems without uncertainties. A separate design principle is developed. Some illustrative examples are given to show the effectiveness and the feasibility of the proposed methods.

In this paper, the adaptive fuzzy tracking control problem is discussed for a class of uncertain multiple-input-multiple-output (MIMO) nonlinear systems with the block-triangular structure. The fuzzy logic systems are used to approximate the unknown nonlinear functions. By using the backstepping technique, the adaptive fuzzy tracking control design scheme is developed, which has minimal learning parameterizations. The adaptive fuzzy tracking controllers guarantee that the outputs of systems converge to a small neighborhood of the reference signals and all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. Two examples are used to show the effectiveness of the approach

We have studied the comment about our original paper and we agree that a minor mistake was made in Eq. 37 of our original paper (see ibid., vol. 11, no. 3, p. 354-60 (2003)).

The adaptive fuzzy control scheme based on observer is proposed for a class of MIMO nonlinear systems whose states are unavailable. By applying "dominant input" concept and combining adaptive control, H/sup /spl infin// control with fuzzy logic systems, the output feedback control law and parameter adaptive law are derived. The whole control scheme can guarantee the stability of the closed-loop, and achieve H/sup /spl infin// tracking performance.

Based on the Lyapunov synthesis approach, many adaptive neural control schemes have been developed during the last few years. So far, most of these schemes have been applied to the classes of uncertain systems whose state variables are assumed to be measurable. This paper develops an adaptive neural control approach that relaxes the restrictive assumption that is usually made by designing a state observer. The overall adaptive neural control scheme is shown to guarantee the stability of the closed-loop system and obtain good tracking performance as well.

In this paper, direct and indirect adaptive output-feedback fuzzy decentralized controllers for a class of uncertain large-scale nonlinear systems are developed. The proposed controllers do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations, and a new hybrid adaptive fuzzy control methodology is proposed by combining the adaptive fuzzy systems with H infinity control and the sliding mode control techniques. Based on Lyapunov stability theorem, the stability of the closed-loop systems can be verified. Moreover, the proposed overall control schemes guarantee that all the signals involved are bounded and achieve the H infinity-tracking performance. To demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.

A hybrid indirect and direct adaptive fuzzy output tracking control schemes are developed for a class of nonlinear multiple-input-multiple-output (MIMO) systems. This hybrid control system consists of observer and other different control components. Using the state observer, it does not require the system states to be available for measurement. Assisted by observer-based state feedback control component, the adaptive fuzzy system plays a dominant role to maintain the closed-loop stability. Being the auxiliary compensation, H/sup /spl infin// control and sliding mode control are designed to suppress the influence of external disturbance and remove fuzzy approximation error, respectively. Thus, the system performance can be greatly improved. The simulation results demonstrate that the proposed hybrid fuzzy control system can guarantee the system stability and also maintain a good tracking performance.

A stable adaptive fuzzy sliding-mode controller is developed for nonlinear multivariable systems with unavailable states. When the system states are not available, the estimated states from a semi-high gain observer are used to construct the output feedback fuzzy controller by incorporating the dynamic sliding mode. It is proved that uniformly asymptotic output feedback stabilization can be achieved with the tracking error approaching to zero. A nonlinear system simulation example is presented to verify the effectiveness of the proposed controller.

Some drawbacks of the aforementioned paper are pointed out, and a new direct adaptive fuzzy control algorithm is suggested for unknown nonlinear systems.

This paper addresses the analysis and the design of fuzzy robust observer for a class of uncertain nonlinear systems on the basis of Takagi-Sugeno fuzzy model, which considers both the states unobservable problem and the uncertainty problem of fuzzy model. It is shown that the designed robust observers possess the stability and the state estimation errors converge to zero.

In this paper, a stable fuzzy direct control scheme is presented for a class of interconnected nonlinear systems with unknown nonlinear subsystems and unknown nonlinear interconnections. In this control algorithm, fuzzy logic systems are employed to approximate the optimal controllers, which are designed on the assumption that all dynamics for each subsystem are known; then the fuzzy controllers and adaptation mechanisms for each subsystem depend only on local measurements to provide asymptotic tracking of a reference trajectory. In addition, a fuzzy sliding mode controller is developed to compensate for the fuzzy approximating errors and attenuate the interactions between subsystems. Global asymptotic stability is established in the Lyapunov sense, with the tracking errors converging to a neighborhood of zero. A simulation example is given to illustrate the performance of the proposed method.