The wastewater treatment process (WWTP) operates under diverse conditions, and precise control of dissolved oxygen (DO) and nitrate nitrogen (NO3-N) concentrations is crucial for satisfying water quality standards. This paper proposes an adaptive fuzzy neural network (FNN) constrained control method based on an event-triggered mechanism. Firstly, the unknown nonlinear dynamic functions encountered in WWTP are effectively approximated using the FNN’s strong adaptive capability. Secondly, an event-triggered control (ETC) strategy is introduced to reduce the communication burden, with trigger conditions designed based on the control signal error. Subsequently, a time-varying asymmetric barrier Lyapunov function (BLF) is used to construct controllers for DO and NO3-N concentrations, ensuring variables remain within time-varying constraint ranges. Meanwhile, a fault-tolerant control (FTC) approach is introduced to cope with potential actuator failures during the WWTP. Finally, simulations using Benchmark Simulation Model 1 (BSM1) are performed to verify the effectiveness of the proposed method.

This paper proposes an adaptive event-triggered tracking control strategy for quarter-vehicle bionic active suspension system with state constraints. Firstly, the crane-leg bionic structure is applied to the suspension design, and a model with ideal nonlinearity and damping characteristics is established, significantly improving the energy efficiency and stability of the system. Secondly, to solve the physical constraint problem of the suspension vertical displacement, an innovative double-layer barrier Lyapunov function (BLF) is adopted, combined with the backstepping method, to strictly limit the state variables within the preset safe range, converting the traditional constrained stability problem into an unconstrained control problem, avoiding the risk of mechanical structure failure. Finally, in response to the challenge of limited communication resources between the controller and the actuator, a combined relative threshold event-triggered control (ETC) strategy is proposed. This strategy significantly reduces the data transmission volume, strictly avoids the Zeno phenomenon, and overcomes the deficiency of insufficient adjustment range of fixed-threshold ETC in bionic suspension systems. Stability analysis proves the stability of the closed-loop system. Simulation results verify that the proposed scheme can effectively improve the stability and comprehensive performance of the vehicle suspension system.

This paper investigates the consensus control problem of multi-agent systems under intermittent communication and unmodeled external disturbances. The main contribution is to overcome the limitation of current synchronous intermittent framework and propose a novel asynchronous intermittent communication methodology on multi-agent systems. In this intermittent methodology, the state space is divided into three distinct regions by introducing both safety and intermittent boundaries, which enables effective monitoring of agent error dynamics.Furthermore, an asynchronous intermittent communication protocol is designed, where the activation and rest intervals are adjusted based on the real-time error states of the agents.By utilizing the distributed extended observer to observe the relative output information and unmodeled disturbances, the novel asynchronous intermittent consensus protocol with disturbance rejection is designed to realize the overall consensus of the multi-agent systems. The proposed spatial-segmentation-dependent intermittent communication methodology can adjust communication and non-communication time of each agent asynchronously according to the communication requirements, under which the multi-agent systems can tolerate more non-communication time and reduce the communication frequency. Finally, numerical simulations are performed to verify our results.

This paper presents an adaptive fuzzy tracking control protocol for a category of uncertain nonlinear multi-agent systems (MASs) subject to deception attacks and multiple constraints (time-varying asymmetry constraints on tracking error and system states). Fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear dynamics in MASs. Since deception attacks over the sensor network make the actual states of the MASs unavailable, this paper employs the compromised states for feedback control. Based on the relationship between the compromised states and actual states, the problem of satisfying the original state constraints boils down to the new constraints on compromised states. The use of a nonlinear mapping together with the dynamic surface control (DSC) strategy can ensure that the multiple constraints are solved with the constraint boundaries of system output being freely selected by the user, the feasibility requirement on the virtual controller is removed, and the computational explosion is mitigated. Under this control protocol, the tracking performance of MASs subject to deception attacks is achieved, while all constraints are not violated. Ultimately, simulation results verify the effectiveness and advantage of the developed control method.

To enhance the control effectiveness and operational efficiency of the wastewater treatment process (WWTP), this article proposes a multivariable optimal control scheme based on an identifier–critic–actor reinforcement learning (RL) framework with an event-triggered mechanism (ETM) for dissolved oxygen (DO) and nitrate nitrogen (NO) concentrations. First, the first fuzzy neural network (FNN) is used to estimate the unknown dynamics in WWTP, and the second FNN is implemented within the critic–actor optimization framework. Second, the RL algorithm is applied to design optimal controllers for DO and NO concentrations by constructing a tangent barrier Lyapunov function. Moreover, a dynamic ETM based on the adaptive threshold strategy is proposed to balance the control performance and energy consumption in the wastewater system. Finally, stability analysis and the benchmark simulation model no. 1 are conducted to verify that the control scheme proposed in this article demonstrates effectiveness and enhanced performance.

In this article, we investigate the adaptive safety-constrained control problem for quadrotor unmanned aerial vehicle (QUAV) clusters in dense forest environments to achieve adaptive navigation and obstacle avoidance. Compared to traditional methods, obstacle avoidance constraints are introduced for the first time, and the limitations of fixed formations and the need for prior data are eliminated. First, a cluster constraint mechanism is developed to constrain the distance between QUAVs within the cluster and the distance between the QUAV and the desired trajectory. Then, considering the lack of targeted obstacle avoidance constraint mechanisms in previous methods and the extensive prior data required by learning-based approaches, an obstacle constraint model is established to ensure that the QUAV maintains a safe distance from obstacles to avoid collisions. Finally, an adaptive safety control strategy for QUAV clusters is proposed by combining constraint conditions and stability criteria. Under the proposed control strategy, the QUAV clusters can achieve stable, safe, and efficient navigation and obstacle avoidance, and all constraints will always be satisfied. Furthermore, a numerical simulation experiment on a QUAV cluster navigation demonstrates the effectiveness and flexibility of this strategy.

A Stackelberg-Pareto differential game-based approximate optimal interaction control approach is proposed for user-led modular robot manipulator (MRM) systems modeled by joint torque feedback (JTF) technique. The major objective of optimal control with physical human-robot interaction (pHRI) is evolved into approximating Stackelberg-Pareto equilibrium by adopting cooperative differential game in MRM and Stackelberg differential game between the human and robot. Learning from adaptive dynamic programming (ADP), the approximate optimal interaction control strategy with pHRI is developed by critic neural network (NN) for solving the coupled Hamilton-Jacobian (HJ) and HJ-Bellman (HJB) equations. The position tracking error under pHRI task is ultimately uniformly bounded (UUB) by the concept of Lyapunov theorem. Two distinction experiments demonstrate the superiority of proposed control approach.

In soft deformable terrain environments, the robot slips due to dynamic changes in wheel-ground contact, which poses a great challenge to the design of the driving torque of its motion control system. To solve the trajectory tracking control problem of wheeled mobile robots in soft deformation terrain, an event triggering mechanism based on wheel-ground mechanical parameters was designed, in which wheel-terrain mechanics has an important influence on the driving torque and is included in the control system design process. Aiming at the wheeled mobile robot in the working environment of soft ground, considering the rolling resistance of the wheel during its driving process, a dynamic model based on wheel-ground interaction is established. Estimation of unmodelled dynamic and rolling resistance terms for wheeled mobile robots in soft deformable terrain environments by adaptive neural networks. Based on the static event triggering strategy based on constant threshold, a hybrid threshold dynamic event triggering strategy based on rolling resistance is proposed. By proving that there is a positive lower bound on the inter-event time, which means that Zeno behavior is avoided. Meanwhile, the lower bound of inter-event time will change with the designed dynamic threshold. Finally, the good control performance of the proposed algorithm under different ground environments is verified by simulation. Note to Practitioners—With the advancement of detection tasks, the working environment of wheeled mobile robots has become increasingly complex. In the motion control of a wheeled mobile robot in a soft deformable terrain working environment, the influence of the robot ’s wheel-to-ground contact is crucial to the successful realization of the task. The existing wheeled mobile robot control methods for soft deformable terrain working environment usually ignores the influence between wheels and ground, which cannot meet the application requirements of this complex scene. Aiming at the problem of tracking control of wheeled mobile robots in soft deformable terrain working environment, this paper, the traction force change caused by wheel-ground contact mechanics is taken as the main factor of event-triggered mechanism, and the force feedback event-triggered tracking control method is designed. Theoretical algorithms and simulation results show that a trade-off between robot tracking performance and communication resources in different ground environments is realized.

In this paper, an adaptive neural network control algorithm based on event-triggered reinforcement learning is proposed for a four-wheel independent steering and four-wheel independent driving (4WS4WD) mobile robot. A kinematic model is established based on the kinematic relationship between the robot wheels and the body under the consideration of the effect of slip-turn perturbation. The dynamics model is established using the Lagrangian dynamics equations. An improved performance metric function is designed and approximated using the Critic neural network and the Actor neural network to approximate the unknown long-term performance metric function and controller respectively. A threshold band event triggering is proposed for reducing the consumption of communication and computational resources. It is rigorously demonstrated using Lyapunov analysis that both the neural network error and the system error are up to the final consistent bound. As well as proved that the proposed event-triggered mechanism can eliminate the Zeno phenomenon. Finally, comparative experiments demonstrated the effectiveness of the proposed algorithm.

In this paper, event-triggered control synthesis of Interval Type-2 Takagi-Sugeno (IT2 T-S) fuzzy interconnected system is investigated via aperiodic intermittent method. Remarkably, time scale differential equation is introduced to construct a hybrid mode of discrete and continuous interconnections. An aperiodic intermittent control mindset is proposed inspired by the system energy attenuation characteristics. What’s more, a novel event-triggered mechanism embedding exponential decay function is developed to help reduce the sampling amount during the work cycle. By establishing time-scale type Lyapunov functions, sufficient criterion is obtained to guarantee stabilization of IT2 T-S fuzzy interconnected system with no Zeno behavior. Finally, some simulations on different time scales are given to verify the effectiveness of the proposed method.

This article considers the hierarchical containment control (HCC) for flexible mirrored collaboration, which accommodates the bipartite cluster consensus behavior in two symmetric convex hulls formed by multiple leaders. First, to achieve the mirrored collaboration in symmetric convex hulls, the layer-signed digraph is generated by involving the antagonistic interaction. Benefiting from the hierarchical structure, the antagonistic interaction in the assistant-layer replaces the assumption of in-degree balance for the existing cluster consensus issues. Second, the existing types of control protocols and the framework of cooperative output regulation limit the achievement of the studied hierarchical mirrored collaboration. To solve this problem, the hierarchical cooperative output regulation is extended based on the formulated hierarchical mirrored collaborative errors. Third, the layer-signal compensator is designed estimating the states of leaders as well as guaranteeing the convergence of collaborative behaviors. Combining with the designed layer-signal compensator, a novel HCC protocol is proposed so that the bipartite cluster consensus behavior can be achieved simultaneously in two symmetric convex hulls. Finally, theoretical results are verified by performing the numerical simulation.

In the soft deformable terrain environment, the running state of the wheeled mobile robot is easily affected by the complex wheel-ground interaction, which limits its running state variables and input torque. In this paper, the tracking control of wheeled mobile robot under soft deformable terrain is studied, and a dynamic event trigger mechanism is proposed. Based on the proposed trigger strategy, an adaptive event trigger optimal tracking control algorithm for wheeled mobile robot system with nonlinear constraints is designed. By analyzing the nonlinear constraint problem faced by the dynamic model of wheeled mobile robot considering skidding and slipping, the dynamic model of wheeled mobile robot in soft deformable terrain environment with force-speed mixed constraints is constructed. Combining the force-speed constraint and the state error event-triggered idea, a dynamic event-triggered mechanism containing constraint information is designed, and Zeno behavior is avoided. An adaptive event-triggered optimal controller is constructed by combining adaptive dynamic programming algorithm and policy iteration algorithm. To make the wheeled mobile robot complete the tracking control. Finally, it is verified by simulation.

Taking advantage of high-performance intelligent robots to solve the coordination control problem such as assembly, handling, and installation, transportation is gradually becoming a kind of frontier subject with great scientific research value in the field of robotics. However, due to possible conflicts and inconsistencies between the manipulator and the operating object, it is challenging to design the optimal coordination control scheme between human and robot. This article presents an event-triggered mixed nonzero-sum game optimal control method, which considers both nonzero-sum game and cooperative game cases, for modular robotic manipulator (MRM) systems performing coordinated operation tasks. First, the joint torque feedback technique and joint task assignment method are employed to establish the dynamic model of MRM subsystem, and then, the global state-space description is deduced. For the unknown information containing interconnected dynamic coupling (IDC) terms and friction modeling errors, an adaptive neural network (NN) identifier is established by utilizing the measured input-output data of each joint module. The adaptive updating law guarantees that the NN weight error finally converged to a minimum neighborhood of zero. To ensure the optimality of system overall performance, the corresponding value functions reflecting the interconnectedness among each joint subsystem and manipulated object are constructed. Based on the idea of differential game, the coordination control problem of MRM system is transformed into a mixed nonzero-sum game problem among each joint module and the operated object. Next, by constructing a single critic NN with learning structure, the optimal value function is approximated to solve the event-based Hamiltonian equations, and then, the optimal control strategy of each player is obtained. Finally, the Lyapunov theory is used to analyze system stability, and the effectiveness of the presented method is reinforced by experimental results.

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

This article proposes an adaptive intermittent control and an adaptive optimal control for quarter-vehicle active suspension systems. This article leverages integral-type barrier Lyapunov functions (BLFs) to ensure that the vertical displacement and vertical displacement velocity always satisfy state-related constraints. In order to stabilize the vehicle’s attitude and improve passenger comfort, an adaptive intermittent control method is designed to seek the dwell-time condition, achieving a balance between controllable and uncontrollable subsystems. In addition, to reduce the power consumption of the control input, an adaptive optimal control method is designed by designing optimal cost functions and employing the backstepping algorithm under the framework of actor–critic neural networks (critic NNs). The stability of the quarter-vehicle active suspension system is analyzed based on the Lyapunov theory. Finally, simulation results demonstrate significant effects on passenger comfort and reduced control input power for both control methods.

To address the challenges posed by flight envelope limitation, external disturbances, model uncertainties and actuator failures in quadrotor unmanned aerial vehicles (UAVs), we propose an adaptive neural attitude control method that incorporates a Nussbaum function and nonlinear disturbance observer (NDO). By designing the Nussbaum function, we effectively address potential actuator failures while leveraging the NDO enables us to employ feedforward compensation strategy to mitigate perturbation effects. To handle the flight envelope limitation and model uncertainties, we introduce a nonlinear state-dependent function (NSDF) and neural networks (NNs), respectively. The NSDF is utilized to directly constrain the attitude, while the NNs are constructed to estimate the unknown components. Simulation results demonstrate that this approach successfully addresses the flight envelope limitation and maintains robust tracking performance even in the presence of external disturbances, model uncertainties and actuator failures in the controlled system.

An adaptive irregular constraint control problem is investigated in this study based on an output feedback control strategy. Nonlinear systems with irregular constraints are widely used in engineering fields such as the robot flexible operation. We consider such constraints referring to ones that may not only be asymmetric, but may also emerge in stages, or even be positive and negative at times. Ancillary constraint boundaries, which extend the originally imposed constraints to the full period of the system operation, are designed to accommodate the irregular constraints. Furthermore, the state observer is used to calculate the unmeasured states. Meanwhile, to get past the constraint that the nonlinearities in the system rely exclusively on the measured output, we employ the small-gain approach. Through the utilization of the input-state-practically stability (ISpS) theory, it is demonstrated that when the recommended adaptive control technique is applied, the system is semiglobal stable. Also, the output of the system follows the relevant trajectory. The validation of the findings from the simulation further highlights the advantages of the advised control program.

This article investigates an output consensus control problem for heterogeneous multi-agent systems with switching disconnected networks. As compared to similar works, each follower can measure only part information of the leader’s output in this paper, which lightens the measurement burden of simple agents when the dimension of leader’s output is large-scaled. In this case, due to the coexistence of incomplete measurements of leader’s output and disconnected networks, the outputs of some agents can deviate from the leader though there exists the observer-based control on them. In order to overcome this difficulty, we utilize the theory of switching unstable systems and propose a novel segmented time unit method. With the aid of this method, the switching intervals are segmented into some time units. Then by analyzing the cooperative control rule within the time units, the stabilizing characteristics of switching behaviors can be obtained to offset the divergence during the switching intervals. On this basis, a novel segmented time-varying Lyapunov function is developed to analyze the error states and sufficient criteria for the output consensus are derived. At last, a numerical simulation is shown to verify the theoretical results.Note to Practitioners—Most existing works on switching disconnected networks require that the leader (or the exosystem) is critically stable (or stable). However, unstable high-dimensional leader widely exists in the fields of multi-agent systems, such as the formation control of MASs where the agents are affine functions of time. On this account, this paper studies multi-agent systems with unstable high-dimensional leader under switching disconnected networks. To solve this problem, a novel segmented time unit method is proposed in this paper to study multi-agent systems with switching disconnected networks and incomplete leader measurement. Based on the segmented time unit approach, the observer-based control protocols and switching signals are given to realize the overall consensus. Numerical simulations suggest that this approach is feasible but it has not been tested in production. Future works will consider the formation control problem with switching disconnected networks and incomplete leader measurement.

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

Due to the limited computing and processing ability of modular robot manipulator (MRM) components, such as sensors and controllers, event-triggered mechanisms are considered a crucial communication paradigm shift in resource constrained applications. Dynamic event-triggered mechanism is developing into a new technology by reason of its higher resource utilization efficiency and more flexible system design requirements than traditional event-triggered. Therefore, an optimal control scheme of multiplayer nonzero-sum game based on dynamic event-triggered is developed for MRM systems with uncertain disturbances. First, dynamic model of the MRM is established according to joint torque feedback technique and model uncertainty is estimated by data-driven-based neural network identifier. In the framework of differential game, the tracking control problem of MRM system is transformed into the optimal control problem for multiplayer nonzero-sum game with the control input of each joint module as the player. Then, the static event-triggered control problem of MRM system is studied based on adaptive dynamic programming algorithm. On this basis, the internal dynamic variable describing the previous state of the system is introduced, and the characteristics of dynamic trigger rule and its relationship with static rule are revealed theoretically. By designing an exponential attenuation signal, the minimum sampling interval of the system is always positive, so that Zeno behavior is excluded. Lyapunov theory proves that the system is asymptotically stable and the experimental results verify the validity of the proposed method.

In this article, two novel adaptive fault-tolerant control schemes for a class of nonlinear strict-feedback cyber-physical systems (CPSs) with deception attacks are presented. Deception attacks, such as false data-injection attacks, which destroy sensor networks, make the outputs and states of the CPSs unavailable. It is very difficult and challenging for a designer to achieve the tracking control under the circumstance of cyberattacks. To realize the tracking control for the studied CPSs, we propose a new coordinate transformation technology without precedent, where it takes the attack gains into account and uses the compromised states to design the corresponding controllers. In the backstepping design process, Nussbaum functions are presented to alleviate the influence of the unknown attack gains. Furthermore, we consider the actuator faults problem, which includes the loss of effectiveness and the bias fault. By skillfully designing the adaptive laws, the effect of actuator faults is completely eliminated. It is theoretically proved that the first proposed tracking control scheme can guarantee all signals in the closed-loop system are bounded and the output can track the desired reference signal. In addition, the second adaptive control scheme is also developed for the CPSs under the actuator faults and a more general assumption on the deception attacks is proposed simultaneously. Finally, the feasibility of the new proposed methods is verified by MATLAB simulation analysis.

This article investigates an adaptive fault-tolerant control problem of an automatic flexible robotic manipulator (AFRM) subject to system uncertainties, actuator faults and saturations, and disturbances. By integrating fuzzy logic systems, projection functions, and two novel fuzzy disturbance observers designed for the position and angular loop subsystems, a new adaptive fault-tolerant control scenario is adopted to ensure semiglobal uniform ultimate boundedness for the AFRM. With the introduced control scheme, the oscillation amplitude and angular-displacement tracking error remain within compact sets. At last, simulation results are used to verify the rationality and validity of the developed control strategy.

This article addresses an adaptive consensus control problem for heterogeneous multiagent systems (MASs) with switching disconnected topologies. Unlike the existing works on switching disconnected topologies, the unstable high-dimensional leader is first considered in this work. To tackle this problem, we propose a novel blockwise energy descent approach. This approach divides the switching periods into several time blocks and mines the operation laws of agents within these blocks. Then, the descent phenomenon at switching time can be obtained, which can be used to counteract the divergence within the switching periods. Building upon this, we develop a time-varying Lyapunov function to describe the system's dynamics and establish conditions for achieving the output consensus. Finally, we develop a simulation example to confirm the validity of our theoretical results.

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

This article studies the adaptive control about the geodetic fixed positions and heading of three-degree-of-freedom dual-propeller vessel. During the navigation of a vessel at sea, due to the unpredictable sea, on the one hand, it is important to ensure that the vessel can smoothly follow the desired geodesic fixed position and heading; on the other hand, when the sailing environment is harsh, it is even more important that the vessel can adapt to the desired geodesic fixed position and heading that change at any time for safe driving. Therefore, this article selects the time-varying function related to the desired geodesic fixed position and heading as the constraint condition, and the constraint condition will change in real time as the expected position and heading change. The design of the control strategy is difficult, and the designed control strategy will be more suitable for complex maritime navigation conditions. First, the article constructs a log-type barrier Lyapunov function. Second, by introducing an unknown external disturbance observer, the external disturbances caused by the environment that may be encountered during the vessel's voyage can be observed. Then, combined with the backstepping algorithm, a neural network (NN) control strategy and adaptive law are designed. Among them, for the uncertain function in the process of designing the control strategy, the NN is used to approximate it. Furthermore, through the Lyapunov stability analysis, it is shown that applying the designed control strategy to the vessel system in this article can ensure that the system is closed-loop stable. The final simulation experiment shows the effectiveness of the designed control strategy.

This article deals with adaptive event-triggering control for nonholonomic systems. Based on state feedback, we fulfill the cooperative design of control law and event-triggering strategy. The crucial method is to use the set-valued map to cover the discontinuous set of event sampling. At the same time, combining the set-valued derivative with backstepping technique to achieve adaptive event control and neural networks are used to fit the unknown functions. The nonholonomic constraints of the system are removed by state-scale systematic design. Through transforming the event-triggering control system into a cascade network with two layers of subsystems, the stability of the entire system is proved based on the input-to-state stable small-gain theorem. The proof that Zeno phenomenon does not occur works in two ways: on the one hand, it ensures that the event trigger is effective; on the other hand, it ensures that there are limited jump discontinuities so that adaptive control can be carried out. Finally, the effectiveness of the adaptive event-triggering control method based on the small-gain theorem is verified by simulation.

In this article, the problem of full state constraints for a class of uncertain nonlinear switched systems with time-varying delays under average dwell time is studied, and an adaptive event-triggered mechanism is proposed. The Lyapunov–Krasovskii function (LKF) is employed to solve the trouble caused by time-varying delays, neural networks are selected to approximate the uncertain terms in the system, and the state constraint problem is solved by constructing tan barrier Lyapunov function (Tan-BLF). What’s more, the constraint boundaries considered in this article can be expressed as functions that rely on time and historical information of the system. In addition, the mismatch behavior between subsystem and its controller is also considered. Finally, numerical simulation results verify the availability of the control strategy.

An optimal tracking control system using neural adaptive techniques is introduced for nonlinear systems subjected to time delay and inequality constraints, which is partially uncertain. The nonlinear inequality constraints and partial uncertain time delay of the state are considered in the discrete-time nonlinear system. By transforming the inequality constraint information into augmented system state variables, and using the precompensator method, an augmentation system that contains constraints and transformed controller information is obtained. The Lyapunov–Krasovskii functionals (LKFs) can be used to deal with the partial uncertain state time delay. Subsequently, the optimal controller, the long-term cost function, the uncertain resistance, and system dynamics can be approximated by the action, critic, the disturbance, and the state estimation NNs, and suitable adaptive laws are obtained. Furthermore, the uniform ultimate boundedness (UUB) of the signals in the closed-loop control system can be obtained by the designed near-optimal controller. The inequality constraints are satisfied and the challenge arising from partial uncertain time delay has been successfully addressed, while a numerical simulation verification example is presented.

In this article, the problems of state-triggered sampling and self-triggered tracking control for nonlinear systems with constraints are studied. First, the fuzzy observer is designed for the unknown state. In the presence of state-triggered sampling error, the cooperative design of constraint controller is a key problem to be solved. The median value theorem provides help to solve this problem and an asymmetric state-triggering strategy is presented. In addition, it is proved that the closed-loop signals are input-to-state stable, and the sampling error and tracking error are bounded. Then, a general self-triggered tracking control scheme is presented. In order to compare the control performance of different triggering mechanisms, fuzzy observer and logarithmic barrier Lyapunov function are selected also, and the scheme is designed under the framework of backstepping method. Co-designing controllers and scheduling functions is a key issue, so that the physical implementation benefits from not requiring constant monitoring of the state. Finally, the effectiveness of the proposed method is verified by case study, and the control performance of different triggering mechanisms is compared.

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

This article presents an adaptive fuzzy fixed time time-varying formation control (TVFC) method for uncertain heterogeneous nonlinear multiagent systems (HNMASs) with full state constraints. Meanwhile, both partial loss of effectiveness and bias fault are considered in HNMASs. The fuzzy logic systems are selected as an effective tool to approximate uncertain nonlinear functions. The original constrained states of the systems will be converted to unconstrained states by the nonlinear transformed function. Compared with previous papers, it is the first time to handle the TVFC problem of HNMASs with full state constraints. In addition, formation control based on an adaptive fuzzy fixed time strategy not only ensures fast convergence of the system, but also the convergence time doesn't depend on any initial conditions. The stability of HNMAs is proven by the fixed time stability theory. Finally, a simulation is given to testify the effectiveness of the control method.

In this paper, an adaptive fuzzy control problem is studied for a connected automated vehicles platoon subject to unknown dead-zone input and constraints. To better handle the unknown nonlinear dynamical functions and disturbances, the nonlinear dynamics model is transformed to a new model. Then, the fuzzy logic system (FLS) is used to identify the unknown nonlinear functions. A dead-zone inverse technique is introduced to eliminate the negative effects of the unknown dead-zone input nonlinearity. In the framework of backstepping, the tangent barrier Lyapunov function (BLF) is introduced in this paper, and a distributed adaptive fuzzy control scheme is designed so that the position, velocity and acceleration of the vehicle platoon do not violate the given constrained boundaries. Finally, based on the Lyapunov stability theory, it is noted that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is validated by simulation results.

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

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

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

In this article, an adaptive tracking control method for the bionic active suspension system with the event-triggered mechanism is proposed. In order to achieve the ideal control objectives, a nonlinear suspension system structure is proposed based on the biological inspiration. In the existing research, the suspension system tracking control methods are only aimed at a single part of the mass, respectively. But this article adopts a novel tracking method for the vertical displacement difference, which can track the ideal reference model more accurately. For the sake of alleviating the problem of limited resources in the process of vehicle communication, a control method combined with the events triggering of the relative threshold is proposed. The design of the controller makes the vertical displacement and vertical moving speed of the bionic suspension system close to zero. It can effectively improve the communication efficiency between the actuator and the controller. In the design of this system, all the signals involved are bounded. The Zeno behavior is successfully avoided among the event-triggered control mechanism. Finally, the feasibility and rationality of this method are verified by the simulation analysis of the bionic suspension system.

Though voltage-regulation and current-sharing of distributed generations (DGs) in dc-microgrids have been widely studied, additional communication links or independent modulation circuit should be added to achieve information transmission. To accomplish precise current-sharing/voltage-regulation without additional communication devices, this article proposes a communication-free intelligent edge control regarding voltage and current for dc-microgrids. First, the power-information dual modulation (PIDM) is designed to achieve information exchange among DGs and eliminate additional communication devices. Second, the cooperative control problem with two coupled targets, i.e., accurate voltage-regulation and current-sharing, is converted into a matter of optimal control. Therefore, the voltage-regulation and current-sharing could be solved concurrently. In addition, the control objective function of each DG is switched to provide the optimal controller and minimize the voltage/current control deviation, which is further switched to solve the Hamilton–Jacobi–Bellman (HJB) function. In order to solve this HJB function, which is difficult to obtain analytical solution, an intelligent edge control strategy with PIDM is proposed to solve the HJB function. Therefore, the precise voltage-regulation and current-sharing can be accomplished. Finally, the proposed control approach is verified through simulation results.

Although the cyber-physical system stability is widely studied, scholars focus more on system stability with communication time delay. Therein, grid-connected inverters with the digital control system are regarded as one simplest and typical cyber-physical system. Meanwhile, the switching/sampling frequency of the inverter is always selected as low as possible from an efficiency viewpoint, resulting in unavoidable delay time. This delay time is apt to cause the system instability, which is more prone to severity under weak grid. To this end, this paper provides a minimum switching/sampling frequency for grid-connected inverters. Firstly, the system impedance model with equivalent delay time is constructed, which is based on padé approximate approach. This equivalent delay time consists of three parts, i.e., sampling delay time in cyber/physical level, calculation delay time in cyber level and pulsewidth modulation delay time in physical level, which reflects the cyber-physical interaction impact. Furthermore, the stability forbidden criterion is applied to make the switching/sampling frequency solving process become Hurwitz matrix identification problem through space mappings. Based on these space mappings, an adaptive step search approach is adopted to obtain the minimum switching/sampling frequency. Finally, the proposed approach can well evaluate the system stability under different frequencies through simulation and experiment.

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

This article investigates an adaptive fuzzy tracking control approach via output feedback for a class of switched uncertain nonlinear systems with full-state constraints under arbitrary switchings. The adaptive observer and controller are designed based on fuzzy approximation. The main characteristic of discussed systems is that the state variables are not available for measurement and need to be kept within the constraint set. In order to estimate the unmeasured states, the adaptive fuzzy state observer is constructed. To guarantee that all the states do not violate the time-varying bounds, the tangent barrier Lyapunov functions (BLF-Tans) are selected in the design procedure. Based on the common Lyapunov function method, the stability of considered systems is analyzed. It is demonstrated that all the signals in the resulting system are bounded, and all the states are limited in their constrained sets. Furthermore, the simulation example is used to validate the effectiveness of the presented control strategy.

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

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

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

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

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

This article considers the event-triggered control for the active seat suspension system with time-varying full-state constraints. Consider that communication resources may be limited, this article proposes a dynamic relative threshold strategy to reduce the communication burden of actuator and controller. Compared with the fixed value as a trigger condition, the dynamically changing thresholds as trigger conditions are more general and universal. The time-varying full-state constraint problem is solved by using the barrier Lyapunov function. In addition, the radial basis function neural networks are employed to approximate the unknown terms. Then, all signals in the resulted system are bounded, and the Zeno behavior can be avoided successfully. Moreover, all the system states satisfy their corresponding constraint condition. Finally, the feasibility and rationality of this method are proved by the simulation analysis of a real example of a seat suspension system.

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

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

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

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

This paper proposes a novel cross backstepping technique-based controller design for a class of nonlinear constrained systems with its applications to hyper-chaotic systems. Considering the strict feedback systems with partial time-varying state constraints, we divide the special systems into constrained subsystems and unconstrained subsystems. However, the normal backstepping method is only an effective method structured to control lower-triangular systems. Since the method is strictly limited to the system structure, the previous works cannot solve the problem considered. Thus, we employ the cross backstepping method to solve the problem of partial and alternate time-varying state constraints. For the constrained subsystems, the time-varying barrier Lyapunov function (TVBLF) is employed to ensure that the violation of any time-varying constraint does not occur. Besides, the radial basis function neural network (RBFNN) is used to approximate the uncertainties. Then, based on the stability analysis, it is concluded that the output follows the desired trajectory as closely as possible, all the signals in closed-loop systems are bounded, and the alternate time-varying state constraints are never violated. Finally, the simulation results demonstrate the effectiveness of the proposed strategy.

This article proposes an adaptive finite-time control plan for a nonlinear uncertain continuous stirred tank reactor (CSTR) with time-varying output constraint. The challenge in designing this control plan is how to achieve that system output never exceeding the specified time-varying compact as well as achieves finite-time convergence. By introducing the mean value theorem, the considered CSTR is decomposed to nonlinear systems (NSs) with pure-feedback structure. To deal with time-varying output constraint, tangent barrier Lyapunov function (TBLF) is applied in the adaptive finite-time controller design process. The closed-loop system stability can be identified by the presented adaptive finite-time control approach with the TBLF. Finally, the simulation graphics on CSTR are given to indicate the validity of the presented control approach.

In this paper, an adaptive neural network (NN) constraint control method is studied for a class of uncertain nonlinear nonstrict feedback systems with state constraints. The restrictive assumption that the unknown internal dynamics must possess the monotonically increasing characteristics in previous results is removed. The property of radial basis function (RBF)NNs is used to solve the algebraic loop problem based on the approximation structure. In order to achieve full state constraint satisfactions, the barrier Lyapunov functions (BLFs) are employed in each design procedure. Based on the backstepping and less adjustable parameters techniques, the controllers and the adaptive laws are obtained. By using the Lyapunov stability theory, the boundedness of all signals in the closed-loop system is proved. Therefore, the scheme not only solves the stability problem of the nonstrict feedback system but also overcomes the influence of the state constraint on the control performance. Finally, the effectiveness of the control method is verified by two simulation examples.

A novel adaptive controller for the half-car active suspension systems (ASSs), which can improve the riding comfortability and handling stability of the driver, is proposed in this paper. By using nonlinear mapping, it is demonstrated that the nonlinear ASSs with partial performance constraints are transformed into the novel pure-feedback systems without constraints. By introducing a modified dynamic surface control (DSC) into the Lyapunov function, the adaptive neural network (NN) controller is discussed. The unknown continuous functions are estimated by the NNs, and the boundedness of all signals in the closed-loop systems is guaranteed by the Lyapunov stability theory. Meanwhile, the performance constraints are not violated. Finally, the simulations are performed to clarify and verify the effectiveness of the proposed scheme.

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

This paper investigates the problem of adaptive fault-tolerant tracking control for the multiagent systems (MASs) under the time-varying actuator faults and bounded unknown control input of the leader. On the basis of the local state information of neighboring agents, an adaptive fault-tolerant control protocol, which consists of the adaptive estimation of faults, is constructed to compensate for the loss of actuator effectiveness in the leader-follower consensus of MASs. Moreover, the modification term in the adaptive estimation can avoid high-frequency oscillations. It is shown that the tracking errors converge to a neighborhood around the origin in the presence of actuator faults, and the performance of the tracking problem is improved. Furthermore, the protocol is distributed in the sense that the coupling gains are independent. Finally, two examples are given to show the effectiveness of the proposed control protocol.

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

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

This paper focuses on the adaptive control problem for a class of nonlinear single-input single-output lower triangular systems with partial state constraints and unknown backlash-like hysteresis. To prevent the partial states from transgressing the predefined constrained region, a barrier Lyapunov function is presented, whose values will increase to infinity when any of its parameters grows to a given boundary value. To counteract the effect caused by the backlash-like hysteresis, an auxiliary variable with its adaptive mechanism is introduced in the backstepping technique. At the same time, the output of the considered systems can track the reference signal, and all the variables in the design procedure are uniformly ultimate boundedness. In the end, a numerical example is employed to validate the efficiency of the developed theoretical method.

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

In this paper, a decentralized neural network (NN) output feedback fault tolerant control (FTC) problem is addressed for a class of multi-input multi-output systems with actuator fault. In order to avoid the noncausal problem, the original system is transformed into an input-output expression in accordance with the diffeomorphism theory. Then, in order to establish a quick response to the fault, the fault tolerant controller with minimum learning parameters has been designed such that the semiglobal uniform ultimate boundedness of all the variables in the resulting closed-loop systems can be guaranteed. Finally, the output feedback FTC approach is applied to the interconnected CSTRs, and the comparisons with existing methods are provided to show the effectiveness of the proposed strategy.

In this paper, a novel integral reinforcement learning method is proposed based on value iteration (VI) to design the$H_{\infty }$controller for continuous-time nonlinear systems subject to input constraints. To confront the control constraints, a nonquadratic function is introduced to reconstruct the${L_{2}}$-gain condition for the$H_{\infty }$control problem. Then, the VI method is proposed to solve the corresponding Hamilton–Jacobi–Isaacs equation initialized with an arbitrary positive semi-definite value function. Compared with most existing works developed based on policy iteration, the initial admissible control policy is no longer required which results in a more free initial condition. The iterative process of the proposed VI method is analyzed and the convergence to the saddle point solution is proved in a general way. For the implementation of the proposed method, only one neural network is introduced to approximate the iterative value function, which results in a simpler architecture with less computational load compared with utilizing three neural networks. To verify the effectiveness of the VI-based method, two nonlinear cases are presented, respectively.

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

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

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

For most existing aperiodic fault diagnosis algorithms of microgrid inverter, because of the common aperiodic processing features, they have relatively higher amount of algorithm startup, calculation, and complexity. These features increase the hardware requirements and realization difficulty, greatly affect the practicability. In order to improve above-mentioned problems, a practical fault diagnosis algorithm is investigated. In this paper, first, aperiodic corrected-second low-frequency processing method is proposed to get aperiodic small low-frequency data (ASLFD) by a simple way in the real time, which greatly reduces the amount of algorithm startup and corresponding calculation. Second, these ASLFD are processed by the real-time normalization method. Next, the degree of asymmetry and distortion degree of root mean square are extracted, respectively. Furthermore, the feature variables and results are realized through the logical operations. Compared with the existing fault diagnosis algorithms, the proposed algorithm has lower amount of startup and calculation, smaller complexity, and easy realization, which are conducive to practical applications. The detailed experimental results and comparisons are shown to validate the proposed algorithm.

This paper is focused on the data-driven model-free adaptive fault detection and estimation (FDE) and fault-tolerant control (FTC) problems for multi-input multi-output (MIMO) discrete-time systems with unknown sensor faults. First, in the light of the compact form dynamic linearization method, the initial systems are transformed into a novel data-based model with only one unknown parameter. Second, a fault estimator is established to detect the sensor faults. Noting that a time-varying residual threshold is developed to determine whether the sensor faults occur or not. Then, the unknown faults are approximated based on the powerful approximation capability of a generalized fuzzy hyperbolic model and the FTC approaches are reconstructed by applying the optimality criterion. In contrast to the previous schemes, the main contributions are twofold: first, it is the first time to solve the FDE and FTC problems for model-free MIMO discrete-time systems; second, the proposed FTC policy is simple to be implemented with reducing computational burden. Finally, two examples are used to demonstrate the effectiveness of the proposed FDE and FTC methods.

This paper is concerned with the robust optimal tracking control strategy for a class of nonlinear multi-input multi-output discrete-time systems with unknown uncertainty via adaptive critic design (ACD) scheme. The main purpose is to establish an adaptive actor-critic control method, so that the cost function in the procedure of dealing with uncertainty is minimum and the closed-loop system is stable. Based on the neural network approximator, an action network is applied to generate the optimal control signal and a critic network is used to approximate the cost function, respectively. In contrast to the previous methods, the main features of this paper are: 1) the ACD scheme is integrated into the controllers to cope with the uncertainty and 2) a novel cost function, which is not in quadric form, is proposed so that the total cost in the design procedure is reduced. It is proved that the optimal control signals and the tracking errors are uniformly ultimately bounded even when the uncertainty exists. Finally, a numerical simulation is developed to show the effectiveness of the present approach.

This paper investigates the problem of optimal fault-tolerant control (FTC) for a class of unknown nonlinear discrete-time systems with actuator fault in the framework of adaptive critic design (ACD). A pivotal highlight is the adaptive auxiliary signal of the actuator fault, which is designed to offset the effect of the fault. The considered systems are in strict-feedback forms and involve unknown nonlinear functions, which will result in the causal problem. To solve this problem, the original nonlinear systems are transformed into a novel system by employing the diffeomorphism theory. Besides, the action neural networks (ANNs) are utilized to approximate a predefined unknown function in the backstepping design procedure. Combined the strategic utility function and the ACD technique, a reinforcement learning algorithm is proposed to set up an optimal FTC, in which the critic neural networks (CNNs) provide an approximate structure of the cost function. In this case, it not only guarantees the stability of the systems, but also achieves the optimal control performance as well. In the end, two simulation examples are used to show the effectiveness of the proposed optimal FTC strategy.

This paper is concerned with a reinforcement learning-based adaptive tracking control technique to tolerate faults for a class of unknown multiple-input multiple-output nonlinear discrete-time systems with less learning parameters. Not only abrupt faults are considered, but also incipient faults are taken into account. Based on the approximation ability of neural networks, action network and critic network are proposed to approximate the optimal signal and to generate the novel cost function, respectively. The remarkable feature of the proposed method is that it can reduce the cost in the procedure of tolerating fault and can decrease the number of learning parameters and thus reduce the computational burden. Stability analysis is given to ensure the uniform boundedness of adaptive control signals and tracking errors. Finally, three simulations are used to show the effectiveness of the present strategy.

An adaptive predefined performance control problem is investigated for a class of multiple-input multiple-output systems with unknown control direction and unknown backlash-like hysteresis nonlinearities by using generalized fuzzy hyperbolic model (GFHM). Compared with the existing methods, the main features are as follows: the prediction error is introduced to construct the adaptive laws, which means that the approximate accuracy of the GFHM is solved; the Nussbaum-type gain is utilized to deal with the unknown control direction, which avoids the requirement of directiona priori; and by transforming the tracking errors into new error variables, the prescribed steady-state and transient performance can be ensured. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are bounded, and the output tracks a desired trajectory, while the tracking errors are confined all times within the prescribed bounds. Finally, two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach. Since the proposed control strategy is only implemented in a healthy case, how to extend the strategy to a faulty case will be a further topic.

In this paper, the main focus is to cope with the fault detection and estimation (FDE) and fault-tolerant control (FTC) issues of nonlinear single input single output model-free system (MFS), while only the input/output data are utilized. First, in accordance with the pseudo-partial-derivative approach, the original system is transformed into a compact form dynamic linearization data model, in which only one parameter is employed. Second, an estimator is developed to detect the fault. A key highlight is the design of a time varying residual threshold. Moreover, an online neural network (NN) approximator is utilized to learn the unknown fault dynamics and an FTC strategy is reconstructed based on the optimality criterion. In contrast to the previous methods, the main features of the proposed method are as follows: 1) the fault related problem is solved for MFS; 2) the number of system parameters is largely reduced; and 3) NNs are utilized to establish a novel fault estimation scheme. Finally, a numerical simulation is provided to show the effectiveness of the proposed FDE and FTC strategy.

This paper concentrates on the reinforcement learning (RL)-based fault-tolerant control (FTC) problem for a class of multiple-input-multiple-output (MIMO) nonlinear discrete-time systems. Both incipient faults and abrupt faults are taken into account. Based on the approximation ability of neural networks (NNs), an RL algorithm is incorporated into the FTC strategy, in which an action network is developed to generate the optimal control signal and a critic network is used to approximate the novel cost function, respectively. Compared with the existing results, a novel fault tolerant controller is proposed based on an RL method to reduce a long-term performance index after a fault occurs. The meaning of minimizing the performance index after a fault occurs in an MIMO system is that waste will be decreased and energy will be saved. Note that the weights of NNs are adjusted online rather than offline. Then, it is proven that the adaptive parameters, tracking errors, and optimal control signals are uniformly bounded even in the presence of the unknown fault dynamics. Finally, a numerical simulation is provided to show the effectiveness of the proposed FTC approach.

A secondary delay partitioning method is proposed to study the stability problem for a class of recurrent neural networks (RNNs) with time-varying delay. The total interval of the time-varying delay is first divided into two parts, and then each part is further divided into several subintervals. To deal with the state variables associated with these subintervals, an extended reciprocal convex combination approach and a double integral term with variable upper and lower limits of integral as a Lyapunov functional are proposed, which help to obtain the stability criterion. The main feature of the proposed result is more effective for the RNNs with fast time-varying delay. A numerical example is used to show the effectiveness of the proposed stability result.

This paper focuses on the composite adaptive tracking control for a class of nonlinear multiple-input-multiple-output (MIMO) systems with unknown backlash-like hysteresis nonlinearities. A dynamic surface control method is incorporated into the proposed control strategy to eliminate the problem of explosion of complexity. Compared with some existing methods, the prediction error between system state and serial-parallel estimation model is combined with compensated tracking error to construct the adaptive laws for neural network (NN) weights. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed-loop systems are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood. Finally, simulation results are provided to confirm the effectiveness of the proposed approaches.

This paper investigates the adaptive actuator failure compensation control for a class of uncertain multi input single out (MISO) discrete time systems with triangular forms. The systems contain the actuator faults of both loss of effectiveness and lock-in-place. With the help of radial basis function neural networks (RBFNN) to approximate the unknown nonlinear functions, an adaptive RBFNN fault-tolerant control (FTC) scheme is designed. Compared with some exist result in which solving linear matrix inequality (LMI) is required, we introduce the backstepping technique to achieve the FTC task. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are bounded and that the output can successfully track a reference signal in the presence of the actuator failures. Finally, simulation results are provided to confirm the effectiveness of the control approach.