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In this article, the distributed containment control schemes are presented for a class of nonlinear heterogeneous high‐order fully actuated multi‐agent systems. First, for each follower, the reference trajectory generator is constructed by using the output information of the neighbor agents. Then, the distributed containment controllers are designed for the system with known nonlinear system function matrices and control gain matrices. Further, since the existence of modeling errors and other uncertain factors, the obtained system model is often not accurate enough, that is, the system function matrix and control gain matrix are actually unknown nonlinear matrices. To tackle these obstacles, we employ the radial basis function neural network method to approximate the unknown nonlinear system function matrices and skillfully construct the controllers combined with the adaptive technology to eliminate the effects of the unknown control gain matrices. The developed control strategies can guarantee that the containment control can be realized and the containment errors can be adjusted to arbitrary precision. In the end, the simulation results on the electromechanical system and robotic system demonstrate the availability and effectiveness of the provided schemes. [ABSTRACT FROM AUTHOR]

This article studies the adaptive state‐feedback control problem of output‐constrained stochastic high‐order nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics. A key nonlinear transformation function is constructed to convert the original output‐constrained stochastic nonlinear system into an equivalent form without any output constraint. By subtly using the SiISS small‐gain condition and fully extracting the characteristics of system nonlinearities, two new control design and analysis methods are developed to guarantee that the closed‐loop system has an almost surely unique solution, all the closed‐loop signals are bounded almost surely, and the equilibrium point is stable in probability without the violation of output constraint. A simulation result is provided to show the effectiveness of this control method. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive fault‐tolerant tracking control problem for nonlinear systems with prescribed performance and input dead‐zone. First, a new composite variable is constructed by using the characteristics of actuator fault and input dead‐zone for the modeling purpose. Second, an adaptive neural network observer is designed to estimate the system states in the presence of inaccurate feedback information. Third, the proposed control strategy effectively counteracts the effects of sensor failure and unknown nonlinear functions, which makes the tracking error confined within the performance boundary and all the signals of the closed‐loop system semi‐globally uniformly ultimately bounded. Finally, an application oriented example is provided to demonstrate the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

Summary: In this article, the adaptive event‐triggered control issue is researched for a kind of switched nonlinear interconnected systems subject to unknown backlash‐like hysteresis and control coefficients. The fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions. To deal with the unknown control coefficients, the Nussbaum method and adaptive control are introduced. The proposed event‐triggered controller can effectively lessen the communication burden, meanwhile, the Zeno behavior is eliminated. It is guaranteed that the system outputs can track the reference signals and all the system signals are semi‐globally uniformly ultimately bounded (SGUUB). Finally, the simulation results verify the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]

This note is devoted to the analysis of adaptive sliding mode control of H∞$$ {}_{\infty } $$/passivity of semi‐Markov jump discrete‐time uncertain singular systems. We consider the constraints of parameter uncertainties, unknown nonlinear functions, and external disturbances throughout the model. Firstly, a novel mode‐independent sliding mode surface is constructed, then the sliding mode dynamic equation under the equivalent controller is obtained. Secondly, by introducing virtual points, several sufficiency criteria are derived for the sliding mode dynamic ensuring H∞$$ {}_{\infty } $$/passive performance and stochastic admissibility with linear matrix inequalities form. Thirdly, the state trajectory can be driven into a switching band containing the origin by adaptive sliding mode control techniques. Finally, the effectiveness of our findings is demonstrated by comparing existing strategies with three simulation examples. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the finite‐time formation tracking control problem for nonholonomic multirobot systems with inputs quantization. The fuzzy logic systems (FLSs) and adaptive method are introduced to approximate unknown nonlinear functions and parameters. Multirobot needs to keep safe and effective communicating range, the barrier function and prescribed performance method are employed to ensure collision avoidance and connectivity maintenance. Then, in order to make each robot more precisely and quickly track referenced leader's trajectory and consider the finite channel bandwidth in practical applications, the travel range of robots can be maintained at more secure region and formation can operate normally within the given bandwidth. By combining the command filter and finite‐time theory, a novel decentralized finite‐time formation asymptotic tracking (FTFAT) control strategy is further proposed based on inputs quantization technology, it guarantees that all signals are bounded and the formation tracking errors asymptotically converge to zero in finite‐time. Finally, the practicability of FTFAT strategy is demonstrated absolutely for nonholonomic multirobot systems. [ABSTRACT FROM AUTHOR]

This study presents a near‐optimal learning‐based approach for sliding‐mode control of uncertain nonsquare nonlinear systems subject to output constraints. To achieve a compromise between safety and optimality, a reinforcement learning algorithm is proposed to compute the near‐optimal values of the sliding manifold coefficients. In the reinforcement learning algorithm, only measured input‐output data obtained by experiments or simulations are employed. Furthermore, the presented method does not require partial knowledge of the system dynamics to initialize the reinforcement learning process. By employing the tuned sliding vector, an adaptive fuzzy sliding‐mode control (AFSMC) input, including a fuzzy term and a robust term, is generated. The fuzzy term is used to approximate an unknown nonlinear function and the robust term is designed for mismatch compensation. To guarantee that the output constraints are not violated, the adaptation laws for obtaining the fuzzy singletons and the bounds of the approximation errors are designed based on the barrier Lyapunov functions (BLF) theorem. The closed loop asymptotic stability is theoretically analyzed in the article, while the effectiveness of the method is assessed in simulation. [ABSTRACT FROM AUTHOR]

Summary: This article investigates the position tracking control problem of permanent magnet synchronous motors (PMSMs) with mismatched disturbances based on adaptive fuzzy gain‐varying finite‐time command filtered backstepping method. First, the anti‐disturbance ability of the system is improved by constructing gain‐varying functions instead of the traditional static gains. Then, the command filter is adopted to overcome the explosion of complexity in classical backstepping method, and the gain‐varying error compensation mechanisms are introduced to reduce the errors produced by command filters. In addition, the finite‐time control technique makes the tracking error converges to a small neighborhood of origin in finite time. The fuzzy logic systems (FLSs) are used to approximate the nonlinear functions with strong coupling of PMSMs systems, and this article further utilizes the characteristics of FLSs to separate the states and handle the coupling of PMSMs systems. Finally, the simulation results prove the validity of the proposed strategy. [ABSTRACT FROM AUTHOR]

This article investigates the consensus problem for uncertain nonlinear multi‐agent systems (MASs) with asymmetric output constraint. Different from BLF‐based constraint consensus tracking control, a novel approach based on nonlinear state‐dependent function is proposed to solve the asymmetric output constraint, which need not convert output constraint into tracking error bound. First‐order sliding mode differentiator is incorporated into each step of backstepping control design to reduce computation burden. Further, in combination of proposed event‐triggered mechanism based on time‐varying threshold, a distributed fuzzy adaptive event‐triggered finite‐time consensus method is developed. It can ensure that the consensus tracking error tends to a small neighbor in a finite time and the asymmetric output constraint of each subsystem is not violated. Two simulations are given to demonstrate the effectiveness of control method. [ABSTRACT FROM AUTHOR]

Summary: This article investigates the adaptive fuzzy event‐triggered practical fixed‐time control for a class of non‐strict feedback high‐power nonlinear systems with completely unknown function. Compared with similar results, the system model considered here is more general, including powers equal to 1 and this article relaxes the restrictions of nonlinear functions. As we all know, high‐power systems have the uncontrollable ability in the process of linearization, so that successfully presented for standard (low‐order) nonlinear systems may fail to work. In the adding one power integrator framework, this article overcomes the difficulty of control design caused by the powers of control input and the relative threshold event‐triggered signal is introduced to reduce the unnecessary waste of communication resources. Then, an adaptive fuzzy event‐triggered controller is designed via backstepping technique, which can ensure that all the closed‐loop signals are practical fixed‐time stability. Finally, numerical simulation and practical example are provided to validate the effectiveness of the presented control algorithm. [ABSTRACT FROM AUTHOR]

Summary: This article elaborates an adaptive fuzzy event‐triggered control design for stochastic nonlinear time‐delay systems with full‐state constraints. The prescribed constraints are ensured by employing barrier Lyapunov function. The fuzzy logic systems are exploited to approximate lumped unknown nonlinear functions. By cleverly choosing Lyapunov–Krasovskii functional, the adverse effect of time‐delay is effectively overcome. Meanwhile, the event‐triggered mechanism is adopted to save communication resource. It is illustrated that all signals of the controlled system are bounded and all states are maintained the prescribed regions at every step of recursive backstepping design. Finally, simulation results elucidate the validity of the devised scheme. [ABSTRACT FROM AUTHOR]

In this article, a command filtering‐based adaptive event‐triggered neural network control scheme is proposed for a class of uncertain switched nonlinear systems with unknown control coefficient and input saturation. First, radial basis function neural networks are used as function approximators to estimate unknown nonlinear functions. Then, an event‐triggering mechanism based on the tracking error is introduced to avoid the over‐consumption of communication resources. Furthermore, command filters are employed to solve the problem of complexity explosion that exists in conventional backstepping control design, and the error compensation signals are designed to reduce the errors caused by the filters. Considering that the unknown control gain and input saturation exist in many practical applications, a Nussbaum‐type function is thus introduced into the controller design to address these challenging issues. Finally, stability of the closed‐loop system is strictly proven under a standard Lyapunov stability analysis framework. The effectiveness of the proposed control scheme is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

This article discusses adaptive preassigned finite-time stability of nonlinear systems with unknown time-varying powers and full-state constraints. By introducing a concept of practical preassigned finite-time stable, constructing finite-time performance functions and nonlinear transformed functions, and integrating high-power and low-power terms into dynamic surface control design, an adaptive state-feedback controller is designed to eliminate the effects of unknown powers and serious unknown parameters in system dynamics, and decrease the computational burden in previous design methods. It is proved that all the signals of the closed-loop system are bounded, asymmetric time-varying full-state constraints are not transgressed, and systemstates converge to a prescribed arbitrarily small region around zero after a preassigned settling time. Two simulation examples show the effectiveness and advantages of this control scheme. [ABSTRACT FROM AUTHOR]

This article studies the issue of command filter-based adaptive fault-tolerant control for a class of nonlinear systems subject to unknown control directions and disturbance. First, the neural network is employed to deal with the nonlinear functions, and the explosion of the complexity problem is handled by the command filter approach. Second, the bound estimation method and the Nussbaum function are utilized to compensate for the influence of the actuator faults and the unknown directions, respectively. Finally, the tracking error signals are guaranteed to converge into bounded compact sets around the origin, and all closed-loop signals are bounded. The effectiveness of the proposed method is illustrated by three simulations. [ABSTRACT FROM AUTHOR]

In this article, the global stabilization issue is discussed for a class of stochastic continuous time‐delay nonlinear systems suffered from unknown control directions and disturbance. Instead of designing the adaptive law online, a control gain is invoked to adapt for the formidable scene of merely continuous but nonsmooth caused by the low‐order, and to deal with the negative effects of disturbance and multiple unknown nonlinear functions where both input and state time delays are taken into account. Then, by utilizing the homogenous domination approach, a delay‐independent controller is designed with a sign function to compensate for the negative impact generated from disturbance and maintain the global asymptotic stability of the closed‐loop system. Finally, a stochastic simulation is supplied to show the validity of the control scheme. [ABSTRACT FROM AUTHOR]

Summary: This article focuses on the finite‐time adaptive fuzzy control problem based on command filtering for stochastic nonlinear systems subject to input quantization. Fuzzy logic systems are employed to estimate unknown nonlinearities. In the control design, the hysteretic quantized input is decomposed into two bounded nonlinear functions, which solves the chattering problem. Meanwhile, an adaptive fuzzy controller is presented by the combination of command filter technique and backstepping control, which eliminates the computational complexity existing in traditional backstepping design. Under the proposed adaptive mechanism, all the closed‐loop signals remain bounded while the desired system performance can be realized within finite time. The main significance of this work is that (1) the filtering error can be solved on the basis of the designed compensating signals; (2) the requirement of adaptive parameters is decreased to only one, which simplifies the controller design process and may improve the control performance. Two simulation examples are used to validity of the developed scheme. [ABSTRACT FROM AUTHOR]

The topic of adaptive event‐triggered control for multi‐input‐multi‐output nonlinear systems with asymmetric state constraints is considered in this article. First, by introducing unified barrier functions method, the initial system is transformed to a non‐constraints system, which brings that the requirement of feasibility conditions could be eliminated and the constraint functions could be relaxed effectively. Then, an adaptive tracking controller is designed by combining some excellent technology, where command filter is utilized to overcome the explosion of complexity, neural network is introduced to approximate unknown nonlinear function, and event‐triggered mechanism is proposed to save communication resources. The designed control scheme can make the outputs of the system to track the target trajectories within a small bounded error range, all signals in the closed‐loop system are bounded, and all states do not escape the state constraints. Finally, practical and comparative examples are given to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This article investigates the fixed‐time consensus tracking control problem for multiagent systems composed of uncertain l‐link robotic manipulators with position and velocity constraints. Fuzzy logic systems are employed to model the uncertain dynamic of the robotic manipulators. In order to cope with the asymmetric yet time‐varying constraints, a nonlinear transformation function is introduced. With the help of the nonlinear transformation function, the original constrained manipulator systems are converted into the equivalent systems without constraint. As long as the boundedness of the state variables in the transformed systems is ensured, the constraint conditions of the original systems are not violated. Then, a fixed‐time adaptive fuzzy control scheme is developed. Under the proposed control method, the consensus tracking error can converge into a small neighborhood of origin in fixed‐time, and all the signals in the closed‐loop systems are bounded. Meanwhile, the motion constraints are not violated all the time. Specially, in view of the property of nonlinear transformation function, it is not necessary to change the control structure when the systems are subjected to no state constraint. Finally, a simulation is presented to illustrate the feasibility and effectiveness of implementing the proposed control algorithms. [ABSTRACT FROM AUTHOR]

Summary: This article focuses on the decentralized adaptive fuzzy fixed‐time fault‐tolerant control issue for the error‐constrained interconnected nonlinear systems with unknown actuator faults possessing dead zone. The unknown nonlinear functions can be modeled via fuzzy logic systems. By utilizing the parameter estimation method, the effect of unknown actuator faults possessing dead zone can be compensated. To guarantee the predefined dynamic performance of state tracking errors, the barrier Lyapunov functions and prescribed performance functions are introduced. Then, a dual‐performance fault‐tolerant control method that can guarantee fast transient performance and predefined performance of state tracking errors is proposed via using the decentralized backstepping technique. In addition, on the basis of the Lyapunov stability theory and the fixed‐time criterion, it is proved that the predefined performance of full‐state errors and the stability of closed‐loop systems can be guaranteed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Summary: In this article, an adaptive fuzzy output feedback control method is presented for nonlinear time‐delay systems with time‐varying full state constraints and input saturation. To overcome the problem of time‐varying constraints, the integral barrier Lyapunov functions (IBLFs) integrating with dynamic surface control (DSC) are applied for the first time to keep the state from violating constraints. The effects of unknown time delays can be removed by using designed Lyapunov‐Krasovskii functions (LKFs). An auxiliary design system is introduced to solve the problem of input saturation. The unknown nonlinear functions are approximated by the fuzzy logic systems (FLS), and the unmeasured states are estimated by a designed fuzzy observer. The novel controller can guarantee that all signals remain semiglobally uniformly ultimately bounded and satisfactory tracking performance is achieved. Finally, two simulation examples illustrate the effectiveness of the presented control methods. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the iteration varying trail lengths problem for high‐order continuous‐time nonlinear systems, where the initial state may deviate from the desired value and the sign of input gain is unknown. First, to deal with the general nonlinear systems, a fuzzy approximation technique is applied for each dimension of the nonlinear function and the backstepping technique is then used for controller design and performance analysis. Moreover, to deal with the randomly varying trial length problem, we introduce a novel composite energy function for the asymptotic convergence analysis. Furthermore, the initial state deviation issue is resolved by introducing an initial state learning protocol such that the initial state tracking error converges to zero asymptotically. Last but not least, the unknown control direction is regulated by applying a Nussbaum function and the analysis in the presence of nonuniform trial lengths is strictly established. Based on these treatments, we prove that the tracking error converges to zero as iteration number increases and all signals are bounded. The effectiveness of the proposed framework is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: This paper considers the problem of adaptive fuzzy output‐feedback tracking control for a class of switched stochastic nonlinear systems in pure‐feedback form. Unknown nonlinear functions and unmeasurable states are taken into account. Fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy observer is designed to estimate the immeasurable states. Based on these methods, an adaptive fuzzy output‐feedback control scheme is developed by combining the backstepping recursive design technique and the common Lyapunov function approach. It is shown that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded in mean square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing appropriate parameters. Finally, a simulation result is provided to show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy. [ABSTRACT FROM AUTHOR]