Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive neural control for multiagent systems with asymmetric time‐varying state constraints and input saturation

This article investigates the leader‐follower consensus problem of a class of non‐strict‐feedback nonlinear multiagent systems with asymmetric time‐varying state constraints (ATVSC) and input saturation, and an adaptive neural control scheme is developed. By introducing the distributed sliding‐mode estimator, each follower can obtain the estimation of leader's trajectory and track it directly. Then, with the help of time‐varying asymmetric barrier Lyapunov function and radial basis function neural networks, the controller is designed based on backstepping technique. Furthermore, the mean‐value theorem and Nussbaum function are utilized to address the problems of input saturation and unknown control direction. Moreover, the number of adaptive laws is equal to that of the followers, which reduces the computational complexity. It is proved that the leader‐follower consensus tracking control is achieved without violating the ATVSC, and all closed‐loop signals are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the control scheme.     

Adaptive fault‐tolerant control of an axially moving system with time‐varying constraints

In this paper, for an axially moving system, with the purpose of suppressing vibration, an adaptive fault‐tolerant control method with time‐varying constraints is investigated. The dynamics of the system are comprised of an ordinary differential equation coupled with a partial differential equation. The method used in our study is known as fault‐tolerant control to process affairs of actuator failures occur. Actual control substitutes for ideal control to regulate the vibration when the actuator occurs undesired failures. Time‐varying constraints are appropriate to cope with the variation range of the performance. Lyapunov function has proven that the adaptive control law is feasible, as well as verifying the exponential stability of the system. Eventually, simulations we have done suggest that the effectiveness of the designed control is feasible.     

Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints

In this paper, an adaptive optimal control strategy is proposed for a class of strict‐feedback nonlinear systems with output constraints by using dynamic surface control. The controller design procedure is divided into two parts. One is the design of feedforward controller and the other is the design of optimal controller. To guarantee the satisfaction of output constraints in feedforward controller, nonlinear mapping is utilized to transform the constrained system into an unconstrained system. Neural‐network based adaptive dynamic programming algorithm is employed to approximate the optimal cost function and the optimal control law. By theoretical analysis, all the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded and the output constraints are not violated. A numerical example illustrates the effectiveness of the proposed scheme.     

Adaptive finite‐time control for nonlinear teleoperation systems with asymmetric time‐varying delays

This paper addresses the adaptive finite‐time control problem of nonlinear teleoperation system in the presence of asymmetric time‐varying delays. To achieve the finite‐time position tracking, a novel adaptive finite‐time coordination algorithm based on subsystem decomposition is developed. By introducing a switching‐technique‐based error filtering into our design framework, the complete closed‐loop master (slave) teleoperation system is modeled as a special class of switched system, which is composed of two subsystems. To analyze such system, a finite‐time state‐independent input‐to‐output stability criterion is first developed for some normal switched nonlinear delayed systems. Then based on the classical Lyapunov–Krasovskii method, the stability of complete closed‐loop systems is obtained. It is shown that the proposed scheme can make the position errors converge into a deterministic domain in finite time when the robots continuously contact with human operator and/or the environment in the presence of asymmetric time‐varying delays. Finally, the simulation results are given to demonstrate the effectiveness. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure‐feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one‐to‐one nonlinear mapping are adopted to transform the pure‐feedback system with different output and state constraints into an equivalent unconstrained pure‐feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time‐varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system.     

Fixed‐time state estimation for a class of switched nonlinear time‐varying systems

This paper deals with the state estimation problem of a class of nonlinear time‐varying systems with switched dynamics. Based on the concept of fixed‐time stability, an observer is designed to reconstruct the continuous state of switched nonlinear time‐varying systems with state jumps, satisfying the minimal dwell‐time condition. Using the past input and output values of the studied system, some sufficient conditions are provided to estimate the state before the next switching. Some numerical results illustrate the effectiveness of the proposed scheme.     

Input‐to‐state stability of nonlinear stochastic time‐varying systems with impulsive effects

This paper considers the input‐to‐state stability, integral‐ISS, and stochastic‐ISS for impulsive nonlinear stochastic systems. The Lyapunov function considered in this paper is indefinite, that is, the rate coefficient of the Lyapunov function is time‐varying, which can be positive or negative along time evolution. Lyapunov‐based sufficient conditions are established for ensuring ISS of impulsive nonlinear stochastic systems. Three examples involving one from networked control systems are provided to illustrate the effectiveness of theoretical results obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive consensus control for stochastic nonlinear multiagent systems with full state constraints

In this paper, the consensus tracking problem is investigated for stochastic nonlinear multiagent systems with full state constraints and time delays. The barrier Lyapunov functions proposed for single‐agent constrained systems are constructively extended to solve the consensus problem for multiagent systems with the full state constraints. Some Lyapunov‐Krasovskii functionals are introduced to compensate for state time delays, which are inherent in the complicated nonlinear systems. Based on the variable separation technique, the difficulty arising from the nonstrict‐feedback structure is overcome. Under a directed communication topology, the distributed neuroadaptive control protocols are proposed to guarantee that all the follower agents follow the trajectory of the leader agent and the full state constraints are not violated. The effectiveness of the proposed distributed adaptive control approach is verified via simulation examples.     

A neural composite dynamic surface control for pure‐feedback systems with unknown control gain signs and full state constraints

This paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results.     

Adaptive fault‐tolerant time‐varying formation tracking for multiagent systems with multiple leaders

In this paper, an adaptive fault‐tolerant time‐varying formation control problem for nonlinear multiagent systems with multiple leaders is studied against actuator faults and state‐dependent uncertainties. Simultaneously, the followers form a predefined formation while tracking reference signal determined by the convex combination of the multiple leaders. Based on the neighboring relative information, an adaptive fault‐tolerant formation time‐varying control protocol is constructed to compensate for the influences of actuator faults and model uncertainties. In addition, the updating laws can be adjusted online through the adaptive mechanism, and the proposed control protocol can guarantee that all the signals in the closed‐loop systems are bounded. Lyapunov‐like functions are addressed to prove the stability of multiagent systems. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

状态与输入受限的二阶多输入多输出非线性系统自适应控制

针对含有状态和输入受限的二阶多输入多输出非线性系统的控制问题,提出了一种自适应控制策略.通过综合利用障碍Lyapunov函数和动态面控制方法的特性,使得系统的状态满足约束条件而且能够减少计算量.此外,为了处理输入约束和系统中的不确定性的影响,分别设计了辅助系统和自适应算法.通过理论分析表明,闭环系统的所有状态都是有界的,而且系统的状态和输入都满足约束条件.最后,通过一个数值仿真算例和一个实际的航天器姿态控制系统的仿真来验证所提出的自适应控制策略的有效性.     

Neural adaptive global stability control for robot manipulators with time‐varying output constraints

In this paper, a novel adaptive control scheme is proposed based on radial basis function neural network (RBFNN). The considered system is deduced by the structure of RBFNN with nonzero time‐varying parameter that installed in the fore‐end and terminal of RBFNN. With this structure and the Taylor expansion of any smooth continuous nonlinear function, a universal approximation of RBFNN is addressed according to the analysis of the character of continuous homogenous function and the Euler's theorem. The approximation accuracies can be adjusted online by the nonzero time‐varying parameter in the device with the degree of continuous homogenous function, which expand the semiglobally stability to global stability over conventional neural controller design approaches. Based on the theory analysis of barrier Lyapunov function, the violation of time‐varying constraints can be subjugated without wrecked. Finally, simulation results are carried out to verify the effectiveness by the design methods.     

含高阶干扰的非仿射非线性系统自适应跟踪控制

本文考虑了一类带有高阶干扰和未知参数的非仿射非线性系统的自适应跟踪控制问题.为了提高系统的抗干扰性能,首先设计了扩张状态滤波器估计系统受到的高阶干扰,并把干扰估计值引入到控制器中.其次,在每一步递推设计中,为了避免backstepping方法固有的"微分爆炸"问题,引入滑模微分器估计虚拟控制律的微分,进而提出了一种新的自适应控制策略.借助Lyapunov函数理论方法分析了闭环系统的稳定性,即在所提控制策略作用下,可保证闭环系统所有信号是一致最终有界的.最后,利用MATLAB仿真验证了方法的有效性.     

Adaptive quantized tracking control for uncertain switched nonstrict‐feedback nonlinear systems with discrete and distributed time‐varying delays

This paper is concerned with an adaptive tracking problem for a more general class of switched nonstrict‐feedback nonlinear time‐delay systems in the presence of quantized input. The system structure in a nonstrict‐feedback form, the discrete and distributed time‐varying delays, the sector‐bounded quantized input, and arbitrary switching behavior are involved in the considered systems. In particular, to overcome the difficulties from the distributed time‐varying delays and the sector‐bounded quantized input, the mean‐value theorem for integrals and some special techniques are exploited respectively. Moreover, by combining the Lyapunov‐Razumikhin method, dynamic surface control technique, fuzzy logic systems approximation, and variable separation technique, a quadratic common Lyapunov function is easily built for all subsystems and a common adaptive quantized control scheme containing only 1 adaptive parameter is proposed. It is shown that the tracking error converges to an adjustable neighborhood of the origin whereas all signals of the closed‐loop systems are semiglobally uniformly ultimately bounded. Finally, 2 simulation examples are provided to verify the feasibility and effectiveness of the proposed design methodology.     

Output regulation of time‐varying nonlinear systems

This paper considers the robust output regulation problem for time‐varying nonlinear systems with a time‐varying exosystem. A framework for converting the problem into a stabilization problem of an augmented system is established. The problem is solved for a class of time‐varying output feedback systems with a time‐varying exosystem. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stabilization of nonlinear uncertain systems with stochastic actuator failures and time‐varying delay

In this paper, we investigate the adaptive state‐feedback stabilization problem for a class of nonlinear systems subject to parametric uncertainties, time‐varying delay, and Markovian jumping actuator failures. First, some fundamental results, including the infinitesimal generator and conditions for the existence and uniqueness of the solution, are established for nonlinear systems w.r.t. Markovian vector and time‐varying delay. Subsequently, corresponding stability criterion is generalized to the considered systems. By employing the backstepping method and the tuning function technique, a systematic adaptive fault‐tolerant control scheme is proposed, which guarantees the boundedness in probability of all the closed‐loop signals. It is noted that no fault detection and diagnostic block are needed, and the control law can be adapted automatically by taking account of the innovative state information. The efficiency of the designed controller is demonstrated by an illustrative example. Copyright © 2015 John Wiley & Sons, Ltd.     

Guaranteed cost control of distributed parameter networked control systems with time‐varying delay

Distributed parameter networked control systems mean distributed parameter systems are controlled through a network, where the control loops are closed. In this paper, the problem of guaranteed cost and state feedback controller design is investigated for a class of distributed parameter networked control systems. With the network factors, such as transmission delays, data packet dropouts considered, the distributed parameter networked control system is modeled as a linear closed‐loop system with time‐varying delay and uncertain parameters. By selecting an appropriate Lyapunov‐Krasovskii function and using linear matrix inequality (LMI) approach, the controller is designed to render the system stable and it can keep the cost function less than a certain upper value. In addition, numerical simulation is included to demonstrate the theoretical results.