This paper investigates the robust adaptive predefined-time trajectory tracking control issue for underwater tracked robot with unknown track slipping and unknown dead-zone input. Fuzzy logic system (FLS) is employed to approximate the unknown nonlinear dynamic. A pair of parameter adaptive laws is designed to counteract the effects of unknown track slipping. To ensure that the trajectory tracking error converges to a specified accuracy within a predefined time, a predefined-time performance function is designed. Then, a barrier Lyapunov function (BLF) is constructed by embedding the performance function to avoid the singularity problem. In addition, a disturbance observer is constructed to observe and compensate for hydrodynamic disturbances present in the system dynamics, while a dynamic event-triggered mechanism is proposed to alleviate the computational load and reduce the actuator update frequency. Under the adaptive backstepping recursive design framework, a predefined-time event-triggered robust adaptive trajectory tracking control algorithm with performance constraints is proposed, which ensures system stability while enforcing predefined performance on the tracking error. Finally, the effectiveness and superiority of the proposed control scheme are validated through comparative simulations and data analysis.

This article addresses the resilient cooperative optimal output regulation (COOR) control problem for nonlinear strict-feedback multiagent systems (MASs) under denial-of-service (DoS) attacks. By constructing the resilient adaptive distributed observers, the leader's dynamics and states can be estimated by each follower. In the control design, a control input constructed by feedforward and feedback control input is proposed based on the system data. Neural networks (NNs) are employed to learn solutions of the feedforward and optimal feedback control problems. Meanwhile, to handle the influence caused by unknown nonlinear dynamics, combining off-policy integral reinforcement learning (IRL) algorithm with actor-critic NNs (A-C NNs), an optimal feedback security control law is designed. To illustrate the feasibility and effectiveness of the proposed optimal control strategy, numerical and practical simulation examples are provided. Unlike prior studies limited to linear systems, this work explicitly accounts for complex nonlinear dynamics, significantly broadening the applicability of resilient COOR control problem in real-world applications.

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 article investigates the dynamic event triggered fuzzy adaptive secure control issue for nonlinear vehicle platoon system under stochastic FDI attacks and switching topology. First of all, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear dynamics. By the aid of the prescribed performance functions, the local spacing errors can be constrained within a preset region. By adopting the mathematical expectation method, the stochastic FDI attack signals can be solved. Secondly, under the framework of backstepping control, by constructing the dynamic event-triggering mechanisms, as well as the prescribed-performance technique, a robust intelligent adaptive performance constraint event-triggered secure platoon control algorithm is developed. Via Lyapunov stability theory and Barbalat’s Lemma, the developed control strategy can ensure all signals of the whole platoon system are bounded, and the following vehicles can asymptotically track the leading vehicle. In addition, the individual and string stabilities can also be guaranteed. Finally, the simulations are provided to further validate the feasibility and effectiveness of the proposed control strategy and theory.

The resilient cooperative control issue for uncertain multi-Euler-Lagrangian (EL) systems under a locally-finite number of adversaries that may arbitrarily manipulate communication links is investigated in this paper. We propose a resilient distributed backstepping control strategy and characterize the corresponding necessary and sufficient condition to guarantee the asymptotic consensus to the target state regardless of arbitrarily injected malicious communication information. To restrain the impacts of adversaries, the filtered coordinate-based weighted Mean-Subsequence-Reduced (CW-MSR) mechanism is adopted, which induces the unknown topology switching and may cause the discontinuity of the virtual controls when applying the backstepping method. To overcome the difficulty, locally uniform adjacency weights are selected in the CW-MSR mechanism, and consequently the continuity of the (non-smooth) virtual controls is ensured even in the presence of the topology changes. The non-smooth analysis method is given to prove the asymptotic consensus for the considered system.

This article considers the issue of fuzzy adaptive dynamic event triggered output feedback consensus control for nonlinear multiagent systems (MASs) suffered from stochastic false data injection attacks. First, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions. By estimating the unknown attack signals, a novel fuzzy state observer is proposed. Based on the fuzzy state observer, a robust adaptive fuzzy secured dynamic event triggered control method is developed, where the dynamic surface control technique (DSC) is used to solve the computational complexity problem in backstepping design. The proposed control method ensures that each agent can observe system’s states well, the consensus tracking errors and output tracking errors converge to a small neighborhood of the origin, and all signals in the closed-loop system keep bounded. Finally, simulation results are provided to verify the effectiveness of the proposed control method.

In this article, a fuzzy adaptive prescribed-time performance constrain containment control issue is researched for nonlinear multi-agent systems (MASs). The original system’s prescribed time control issue will be converted into the corresponding controlled system’s asymptotic tracking control issue by using the time-domain mapping technique. Fuzzy logic systems (FLSs) are ultilized to identify the unknown dynamics. Combining prescribed-performance control and time-domain mapping techniques, a fuzzy adaptive prescribed-time performance constraint containment control algorithm is proposed, which can demonstrate that all signals in controlled system are bound within prescribed-time, and followers can converge to the convex hull created by the leaders by using Lyapunov stability theory. Furthermore, the virtual errors and local containment error asymptotically converge to a preset region. Finally, the simulations are provided to illustrate the effectiveness and feasibility of the developed control method. Note to Practitioners—This article investigates a fuzzy adaptive prescribed-time containment control issue for nonlinear multi-agent systems (MASs). The time-domain mapping technique can be used to convert the prescribed time control issue of the original system in finite horizon into the asymptotic tracking control issue of the corresponding controlled system in infinite horizon. In contrast to previous similar works, this article proposes a prescribed-time control algorithm, where the convergence time can be set offline and it does not rely on any design parameters. Moreover, this study can guarantee containment and virtual errors converge to the prescribed region by using the prescribed performance function and the barrier Lyapunov function.

This article studies the fuzzy adaptive resilient output control for nonlinear multi-agent systems (MASs) under Byzantine attacks. Firstly, fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, then a fuzzy state observer is constructed to identify the unmeasured states in the controlled system. The mean-subsequence-reduced (MSR) technique is introduced to filter the unavailable neighbor information of each agent. On the basis of the distributed backstepping technique, a special Nussbaum function is utilized to construct an attack compensation scheme. Combining the compensation scheme and MSR technique, an observer-based robust fuzzy adaptive resilient output control design algorithm is proposed. The developed resilient control method enables the system outputs follow a given protocol under Byzantine attacks. Finally, the feasibility and effectiveness of the proposed control method and theory can be illustrated via the simulation results. Note to Practitioners—In this article, an observer-based resilient fuzzy adaptive output control issue is studied for nonlinear multi-agent systems subjected to Byzantine attacks. Fuzzy state observer is constructed to identify the unmeasured states. Since there exist the Byzantine attacks in the controlled system, the neighbor information of each agent cannot be fully used in the controller design. Thus, compared with the existing related results, the mean-subsequence-reduced technique can be introduced in this article to filter the unavailable neighbor information of each agent. Besides, an attack compensation control method via a special Nussbaum function is designed to resist the effect of uncertainties and malicious data caused by attacks. Simulation results ensure the feasibility of the developed resilient control approach and theory.

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 article, the fuzzy adaptive event-triggered consensus control issue is addressed for nonlinear multiagent systems (MASs) under output constraints and Denial of Service (DoS) attacks. First of all, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions. Then, a novel switching observer is constructed to observe the leader's state and handle DoS attacks. With the help of the exponent-dependent barrier Lyapunov functions (BLFs), the system output can be constrained within a preset region. Based on dynamic surface control (DSC) technique, the issue of computational complexity can be effectively avoided. Combining the designed switching observer and relative thresholds, a robust fuzzy adaptive event-triggered controller is developed, which ensures that the consensus output tracking errors converge to a small neighborhood of zero, and all signals in the closed-loop system keep bounded. Moreover, Zeno behavior can be avoided. Ultimately, simulation results are given to validate the feasibility and effectiveness of the proposed control strategy and theory.

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.

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.

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.

This article investigates the data-based cooperative optimal output regulation problem (COORP) for nonlinear strict-feedback multiagent systems (MASs) under an event-triggered mechanism (ETM). By constructing an adaptive distributed observer, each follower can estimate the leader’s dynamic and state. In the control design, a feedforward-feedback control input is proposed based on system data. By utilizing the neural networks (NNs) to learn the solutions of the nonlinear regulator equation and the Hamilton–Jacobi–Bellman (HJB) equation, the feedforward control problem and the optimal feedback control problem can be addressed. Then, an off-policy integral reinforcement learning (IRL)-based optimal cooperative control method is proposed with actor-critic NNs (A-C NNs), and the influence caused by unknown nonlinear dynamics can be handled.FThrough the stability analysis, it is proved that all signals in closed-loop system are uniformly ultimately bounded (UUB), and the system can achieve Nash equilibrium. To demonstrate the effectiveness of the developed optimal control method, a simulation example is provided.

This article examines a neuroadaptive consensus control issue for heterogeneous port uncrewed container transporter (HPUCT) platoon with model uncertainties and actuator saturation. First, a novel robust finite-time estimator, which combines approximation with sliding mode technique, is introduced to approximate the complex nonlinear dynamics and observe external disturbances in HPUCT. The innovative design of the terminal sliding mode surface contributes to achieving stability in state measurement errors within a finite time. Subsequently, utilizing Lyapunov functions, a robust adaptive sliding mode controller is formulated for the consensus control of vehicles, which can ensure internal stability and string stability for the entire vehicle platoon. Additionally, to tackle the issues of saturation, the control strategy is modified by designing an auxiliary system. Finally, comparative simulations confirm the effectiveness of our designed estimator-based robust neuroadaptive consensus controller.

This article delves into the intricacies of adaptive fuzzy event-triggered formation tracking control for nonholonomic multirobot systems characterized by infinite actuator faults and range constraints. To address these issues, we leverage the power of fuzzy logic systems (FLSs) and employ adaptive methods to approximate unknown nonlinear functions and uncertain parameters present in robotic dynamics. In the course of information exploration, the problems of collision avoidance and connectivity maintenance are ever present due to limitations of distance and visual fields. In this regard, we introduce a general barrier function and prescribed performance methodology to tackle constrained range impediments effectively. Furthermore, to reduce the number of controller executions and compensate for any effect arising from infinite actuator failures, robots engage with their leader at the moment of actuator faults using fewer network communication resources yet maintain uninterrupted tracking of the desired trajectory generated by the leader. With the aid of the dynamic surface technology, we propose a decentralized adaptive event-triggering fault-tolerant (ETFT) formation control strategy. We guarantee that all signals are semi-global uniformly ultimately bounded (SGUUB). Ultimately, we demonstrate the practical feasibility of the ETFT control strategy for nonholonomic multirobot systems.

This paper presents a neural optimization-based fixed-time adaptive control scheme for robot systems with unknown dynamics and input saturation. During the process of information exploration, security and control efficiency issues always exist due to the complexity of the system. In this regard, a performance index function is constructed to optimize control performance, and a nonlinear auxiliary compensation system is developed to solve the saturation effect of the actuator. By solving the Hamilton–Jacobi–Bellman (HJB) equation and utilizing fixed-time theory, a fixed-time optimization control scheme is designed within the framework of adaptive dynamic programming. The objective of this scheme is to achieve both optimal performance and rapid convergence. Secondly, universal approximators, namely neural network (NNs), are employed to handle unknown uncertainties through the actor-critic-identifier structure. Among them, the critic network evaluates system performance, the actor network implements control actions, and the identifier network estimates unknown dynamics. Additionally, under the Lyapunov stability criterion and optimization theory, a stability analysis is conducted to demonstrate the feasibility of the devised neuro-optimal fixed-time control scheme and guarantee the convergence of all signals within a fixed-time. Finally, simulations are performed to further validate the effectiveness of the developed control method.

This article investigates an adaptive neural network (NN) control technique with fixed-time tracking capabilities, employing composite learning, for manipulators under constrained position error. The first step involves integrating the composite learning method into the NN to address the dynamic uncertainties that inevitably arise in manipulators. A composite adaptive updating law of NN weights is formulated, requiring adherence solely to the relaxed interval excitation (IE) conditions. In addition, for the output error, instead of knowing the initial conditions, this article integrates the error transfer function and asymmetric barrier function to achieve the specific performance for position error in both steady and transient states. Furthermore, the fixed-time control methodology and Lyapunov stability criterion are synergistically employed in order to guarantee the convergence of all signals in the manipulators to a compact neighborhood around the origin within a fixed-time. Finally, numerical simulation and experiments with the Baxter robot results both determine the capability of the NN composite learning technique and fixed-time control strategy.

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 paper, an adaptive fuzzy logic system (FLS) predefined time tracking control technique is investigated for robot systems with constrained position errors. To this end, a practical predefined time control approach that integrates FLSs learning technique, predefined time stability criterion, tan-type constraint function and the backstepping recursive design is constructed for the first time. Compared with finite/fixed-time control schemes, the upper bound of the convergence time no longer depends on initial conditions or complex design parameters. Instead, it can be predefined by making adjustments to a single relevant control parameter in advance. In order to avoid the violation of constraint boundaries by position tracking errors, a suitable tan-type barrier Lyapunov function is constructed, and rigorous stability is proved derived from constrained predefined time Lyapunov theory. The results demonstrate that the error signals converge to a small range near origin within the user-defined time. Additionally, to compensate for unknown nonlinearity, a new adaptive update law associated with the convergence time control parameter is established. Simulations and experiments on the Baxter robot platform are carried out to confirm the validity and functionality of the devised controller.

This paper investigates the reinforcement learning-based adaptive fuzzy optimization control problem for third-order nonlinear vehicle platoon. The unknown nonlinear dynamic is approximated using fuzzy logic system (FLS). By the aid of prescribed performance technique, the designed quadratic spacing errors can be ensured to remain within a preset region. By constructing barrier type optimal cost function, and employing the actor–critic FLSs construction, a fuzzy adaptive optimization prescribed performance control algorithm is developed, which further verifies the individual stability of each vehicle, and all signals of vehicle platoon system are bounded. In addition, the strong string stability of vehicle platoon system can be ensured using the couple sliding mode surface. Finally, simulations are conducted to demonstrate the effectiveness and feasibility of the proposed results.

In this paper, the security-based adaptive fuzzy control issue is studied for strict feedback multiagent systems (MASs) with actuator failures and DoS attacks. Fuzzy logic systems (FLSs) are applied to approximate unknown nonlinear functions. In order to deal with the discontinuous signals caused by DoS attacks, a distributed filter is constructed. Based on the proposed filter and the backstepping control technique, a security-based robust adaptive fuzzy fault-tolerant controller is designed to compensate for the effect caused by intermittent actuator faults. The proposed control method can ensure the tracking error converges to a small neighborhood of the origin and all signals in the closed-loop system are bounded. Finally, simulation results are given to demonstrate the effectiveness of the proposed control method.

In this paper, an adaptive fuzzy prescribed time formation control problem is studied for nonlinear multi-agent systems (MASs) with input saturation under undirected graphs. Firstly, by introducing time-domain mapping, the original nonlinear MASs is transformed into an equivalent time-varying system. Then, the prescribed time formation control problem of the original system can be further transformed into the asymptotic tracking control problem in the infinite time domain. Secondly, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear dynamics, and the input saturation problem is solved by introducing an auxiliary subsystem. An adaptive fuzzy prescribed time formation control scheme is proposed by combining command filtering technique and backstepping recursive design techniques. By the aid of Lyapunov stability theorem, all signals of the controlled system are bounded, and formation tracking errors asymptotically converge to zero within a prescribed time. In addition, the influence raised by the input saturation can be effectively offset. Finally, the feasibility of the proposed prescribed time formation control scheme can be further verified by a numerical simulation.

This article investigates the finite-time fuzzy adaptive dynamic event-triggered (DET) formation tracking control problem for underactuated unmanned surface vehicles (USVs) subjected to multiple constraints and intermittent actuator faults. The models of USVs contain unknown nonlinear dynamics, so the fuzzy logic systems are employed to estimate them. Meanwhile, considering the frequent updating of actual control input, a DET strategy is designed, which can improve the communication resource utilization. Subsequently, based on the theory of finite-time stability and prescribed performance control technique, a new robust adaptive fault-tolerant control algorithm is presented, which can not only solve the problem of intermittent actuator faults for USVs, but also has the merits of avoiding collision and preserving connectivity. In addition, it also ensures all the signals of the USVs are bounded in finite time. The simulation results can verify the feasibility of the proposed control method.

In this paper, the problem of fuzzy adaptive fixed-time formation control is studied for nonholonomic multirobot systems (NMRSs) subject to unknown dead-zones and multiple constraints. Fuzzy logic systems (FLSs) are used to identify nonlinear NMRSs with uncertain dynamics, and then adaptive technique are utilized to compensate for unknown dead-zones parameters. By combining prescribed performance control (PPC) method, the transient and steady-state performances of the NMRSs are guaranteed, thereby further achieving collision avoidance and connectivity maintenance. On this basis, in order to achieve fixed-time convergence of formation tracking errors and eliminate the effect of unknown dead-zones, a novel adaptive robust fixed-time formation control (FxTFC) strategy is further proposed by introducing fixed-time stability theory and command filter technique. It can avoid the output shafts do not acting for a short time period when the input shafts turn rapidly, ensure the nonlinear NMRSs are fixed-time stable and all signals are bounded, which can be proved by constructing the Barrier Lyapunov Functions (BLFs). In the end, the simulation studies are carried out to show the efficacy of the developed robust FxTFC strategy. The result is that even if there are actuator dead-zones among each robot, formation tracking can also be achieved in fixed-time.

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.

In this article, the problem of adaptive command filter formation asymptotic tracking control (FATC) is investigated for nonholonomic multirobot systems (NMRSs) with multiple constraints. Consider the robot’s uncertain dynamics parts that the unknown system parameters and nonlinear functions, which are approximated by using adaptive technique and fuzzy logic systems (FLSs). The transient and steady-state performance, collision avoidance, and connectivity maintenance can be guaranteed by employing the universal barrier function and prescribed performance control (PPC) approach. In addition, in order to compensate the influence of filtering errors and make followers more accurately and swiftly track leader’s trail, a novel adaptive FATC scheme is further developed by subtly combining the command filter technique and exponential decay function. This scheme can guarantee all signals of controlled systems are bounded and the formation tracking errors asymptotically converge to origin. Finally, the feasibility of FATC scheme is demonstrated for NMRSs.

In this article, an adaptive neural network (NN) predefined-time tracking control strategy is investigated for robot systems with external disturbance. First, under the predefined-time stability criterion, a new time-controlled torque controller is constructed, which allows for the system convergence time to be set beforehand. This is conducive to manipulators performing trajectory tracking tasks that require specific convergence times. In addition, the continuous terms are constructed by smoothly switching between the fractional and cubic terms of state-dependence. This solution successfully resolves the issues of singularity. Moreover, in order to compensate for unknown nonlinearity and torque disturbance, two different adaptive update laws are established, respectively. Furthermore, rigorous stability is proved based on the predefined-time Lyapunov theory. Finally, the accuracy and efficiency of the NN-based predefined-time control algorithm is confirmed and validated through both numerical simulations and practical experiments conducted with the Baxter robot.

This article concentrates on the disturbance observer-based fuzzy adaptive prescribed constraint control issue for nonlinear third-order vehicular platoon systems. Fuzzy logic system (FLS) is driven to identify unknown nonlinearity. By designing a novel time-varying performance function without using the initial conditions, the proposed quadratic spacing error policy can guarantee the spacing error remains within a residual set with the predefined convergence rate. By constructing a disturbance observer, the restrictive assumptions about the unknown boundaries of the external disturbance and identify error. Then, combining time-varying performance function and constructed disturbance observer, a new robust fuzzy adaptive performance constraint control approach is presented, which demonstrates the individual stability, and the boundedness of all signals of vehicular platoon systems are able to be ensured. Moreover, the string stability of the vehicular platoon systems can also be guaranteed via sliding mode technique. Eventually, simulation results are displayed to explain the validity of the developed prescribed performance platoon control approach.

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.

This article investigates the distributed fuzzy optimal consensus control problem for state-constrained nonlinear strict-feedback systems under an identifier-actor-critic architecture. First, a fuzzy identifier is designed to approximate each agent's unknown nonlinear dynamics. Then, by defining multiple barrier-type local optimal performance indexes for each agent, the optimal virtual and actual control laws are obtained, where two fuzzy-logic systems working as the actor network and critic network are used to execute control behavior and evaluate control performance, respectively. It is proved that the proposed control protocol can drive all agents to reach consensus without violating state constraints, and make the local performance indexes reach the Nash equilibrium simultaneously. Simulation studies are given to verify the effectiveness of the developed fuzzy optimal consensus control approach.

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.

This article focuses on the practically predefined-time adaptive fuzzy quantized control for nonlinear stochastic systems with actuator dead zone. Fuzzy logic systems are employed to approximate uncertain nonlinear functions. A novel stochastic predefined-time control scheme is proposed, which can help reduce the control parameters and increase the robustness of the closed-loop system. Taking the quantization and dead zone in the control link into account, the adaptive parameters and a part of the control are used to estimate and compensate the nonlinear disturbance, respectively. In addition, under reasonable assumptions, the complexity of the Lyapunov function compared with conventional stochastic adaptive control is reduced. Based on the stochastic predefined-time stabilization theory, an adaptive fuzzy controller is designed to make the upper bound of the expected settling time arbitrarily configured. Finally, two examples show the effectiveness of the main results.

In this article, we consider the problem of resilient distributed optimal coordination for uncertain nonlinear multiagent systems, where each agent is remotely dominated by an associated instruction generator via an unreliable network channel, which may be distorted by false data injection (FDI) attacks. To avoid evaluating the quality of decision variable or computing its high-order derivatives when applying the backstepping method, which is difficult in a distributed way, a new two-layer integrated design protocol with a fuzzy-approximation-based adaptive dynamics compensation mechanism is designed. Through the local online estimation of the optimal solution and design of adaptive feedback gain, the fuzzy adaptive mechanism realizes the mutual compensation of cyber dynamics and physical dynamics. Resultantly, all the agents are shown to achieve the optimal consensus regardless of the FDI attacks and nonlinear uncertainties.

This article investigates the problem of fuzzy adaptive predefined-time terminal sliding mode (TSM) control for a third-order heterogeneous vehicular platoon system with an unknown dead zone. For the purpose of approximating unknown nonlinear functions, fuzzy logic systems (FLSs) are utilized. In addition, the impact of the dead zone on the performance of the control may be lessened by building the dead-zone compensation. A tracking error based on the modified constant time headway policy is built to get rid of the assumption of zero initial spacing and decrease the distance between vehicles at the same time. A unique nonsingular TSM control system is then built using the predefined-time stability criterion; with the help of Lyapunov functions, it is possible to demonstrate both the individual and the string stability of the whole heterogeneous vehicle platoon in a predefined time. Finally, a series of simulations are shown to demonstrate the validity of the proposed results.

This paper studies the inverse optimal formation control problem for heterogeneous Euler-Lagrange systems. In order to reduce the impacts of surface vehicles configuration and surface vehicles type on transportation efficiency, the nonlinear terms in the system models are considered. Then, an inverse optimal formation controller is proposed by using leader-follower formation approach and the inverse optimal stability theory, which ensures all signals of considered system are semi-globally uniformly ultimately bounded (SGUUB). And the controller can also minimize the cost function. Finally, a simulation example is given to verify the effectiveness of the designed control method.

This article investigates the problem of adaptive neural network (NN) optimal consensus tracking control for nonlinear multiagent systems (MASs) with stochastic disturbances and actuator bias faults. In control design, NN is adopted to approximate the unknown nonlinear dynamic, and a state identifier is constructed. The fault estimator is designed to solve the problem raised by time-varying actuator bias fault. By utilizing adaptive dynamic programming (ADP) in identifier-critic-actor construction, an adaptive NN optimal consensus fault-tolerant control algorithm is presented. It is proven that all signals of the controlled system are uniformly ultimately bounded (UUB) in probability, and all states of the follower agents can remain consensus with the leader's state. Finally, simulation results are given to illustrate the effectiveness of the developed optimal consensus control scheme and theorem.

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.

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 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 neural-network (NN) output-feedback control problem is investigated for a quarter-car active suspension system. The sprung mass and the suspension stiffness in the considered suspension system are unknown, and the part states are not measured directly. In the control design, NNs are employed to approximate the unknown nonlinear dynamics, and an NN state observer is given to estimate the immeasurable states. By using the adaptive backstepping control design technique and introducing the command filter method, an observer-based NN output-feedback control algorithm is developed, in which the input saturation constraint is compensated via constructing an auxiliary system. It is proved that all the variables of the controlled system are bounded, and the ride comfort, ride safety condition, and suspension space limit are guaranteed. The computer simulation and compared results further show the effectiveness of the proposed control algorithm.

This article investigates the problem of adaptive fuzzy optimal distributed consensus control for stochastic multiagent systems (MASs) with full-state constraints and nonaffine nonlinear faults. Fuzzy logic systems are employed to identify the unknown nonlinearities. To solve the problem of optimal state constraint control, a barrier Lyapunov function based optimal cost function is designed. By introducing Butterworth low-pass filter into control design, the deleterious effects raised by nonlinear fault can be compensated. By utilizing adaptive dynamic programming algorithm in critic–actor construction, a fuzzy adaptive distributed optimal consensus fault-tolerant control method is proposed, which can ensure that all signals of the controlled system are semiglobally uniformly ultimately bounded in probability, and outputs of the follower agents keep consensus with the output of leader. In addition, system states are all not exceeded their constrained bound. Finally, simulation results are provided to illustrate the feasibility of the developed control method and theorem.

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.

This article proposes a sampled-data adaptive fuzzy decentralized output feedback control method for the uncertain nonstrict feedback large-scale interconnected systems whose nonlinear functions are completely unknown and whose states are unavailable for control design. With the help of fuzzy logical systems in identifying the unknown nonlinear functions, and by considering the sampling strategy, a novel sampled-data nonlinear state observer has been designed to approximate the immeasurable state variables, which only contains the output sampling information of the system to be controlled. Furthermore, to avoid the problem of “explosion of complexity” caused by the frequently using the derivative of the virtual controller, the nonlinear filter has been considered under the strategy of the sampled data. Based on Lyapunov theory, a sampled-data adaptive fuzzy decentralized output feedback backstepping control strategy was proposed under the framework of recursive design and sampled-data strategy. The designed sampled-data controller is able to guarantee that all closed-loop signals are semiglobally uniformly ultimately bounded. Two simulation examples are eventually provided to validate the effectiveness of the theoretical findings.

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 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 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.

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.

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.

In this article, the leader-following consensus problem via the event-triggered control technique is studied for the nonlinear strict-feedback systems with unmeasurable states. The follower's nonlinear dynamics is approximated using the fuzzy-logic systems, and the fuzzy weights are updated in a nonperiodic manner. By introducing a fuzzy state observer to reconstruct the system states, an observer-based event-triggered adaptive fuzzy control and a novel event-triggered condition are designed, simultaneously. In addition, the nonzero positive lower bound on interevent intervals is presented to avoid the Zeno behavior. It is proved via an extension of the Lyapunov approach that ultimately bounded control is achieved for the leader-following consensus of the considered multiagent systems. One remarkable advantage of the proposed control protocol is that the control law and fuzzy weights are updated only when the event-triggered condition is violated, which can greatly decrease the data transmission and communication resource. The simulation results are provided to show the effectiveness of the proposed control strategy and the theoretical analysis.

This article studies the problem of adaptive fuzzy fixed-time decentralized control for nonlinear interconnected systems with stochastic disturbances and unknown nonlinearities. In control design, fuzzy logic systems are utilized to identify the unknown nonlinear functions. Combining stochastic fixed-time Lyapunov stability theory with adaptive backstepping control technique, a fuzzy adaptive fixed-time decentralized control design algorithm is developed by adopting smooth projection operator. It is proved that all the state variables of the closed-loop system are globally fixed-time stable in probability. Finally, both numerical and practical examples are provided to elucidate the feasibility of the proposed control algorithm.

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 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 addresses the problem of finite-time neural network (NN) adaptive dynamic surface control (DSC) design for a class of single-input single-output (SISO) nonlinear systems. Such designs adopt NNs to approximate unknown continuous system functions. To avoid the "explosion of complexity" problem, a novel nonlinear filter is developed in control design. Under the framework of adaptive backstepping control, an NN adaptive finite-time DSC design algorithm is proposed by adopting a smooth projection operator and finite-time Lyapunov stable theory. The developed control algorithm means that the tracking error converges to a small neighborhood of origin within finite time, which further verifies that all the signals of the controlled system possess globally finite-time stability (GFTS). Finally, both numerical and practical simulation examples and comparing results are provided to elucidate the superiority and effectiveness of the proposed control algorithm.

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.

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 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.

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 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.

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 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, 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 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.

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.

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.

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.

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, 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.

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.

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 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.

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.

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.

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.

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.

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.

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.