Observer-based adaptive fuzzy tracking control for a class of MIMO nonlinear systems with unknown dead zones and time-varying delays

The adaptive tracking control strategy is investigated for a class of multi-input and multi-output pure-feedback nonlinear delayed systems with unknown dead-zone inputs. This problem is challenging due to the existence of unknown dead zones, time-varying delays and unavoidable state variables. By constructing fuzzy approximators and state observers, the difficulties from unknown nonlinearities and unavailable state variables are surmounted, respectively. Lyapunov–Krasovskii functions are introduced to deal with the time-varying delays. The adaptive controllers are designed by a backstepping method and adaptive technique so that the closed-loop systems remain stable and the target signals can be tracked within a small error as well. At last, two examples are provided to show the effectiveness of the proposed scheme.     

Adaptive fault diagnosis and fault-tolerant control of MIMO nonlinear uncertain systems

This article presents an integrated fault diagnosis and fault-tolerant control (FTC) methodology for a class of nonlinear multi-input–multi-output systems. Based on the fault information obtained during the diagnostic procedure, an FTC component is designed to compensate for the effect of faults. In the presence of a fault, a baseline controller guarantees the boundedness of all the system signals until the fault is detected. After fault detection and then again after isolation, the controller is reconfigured to improve the tracking performance using online fault diagnostic information. Under certain assumptions, the stability and tracking performances of the closed-loop system are rigorously investigated. It is shown that the system signals always remain bounded and the output tracking error converges to a neighbourhood of the origin of the state space.     

Direct adaptive fuzzy control for a class of MIMO nonlinear systems

This article presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time multi-input multi-output nonlinear (MIMO) dynamic systems. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller that can achieve control objectives. The adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking errors are bounded and converge to a neighborhood of the origin. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.     

Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems

In this paper,a new fuzzy adaptive control approach is developed for a class of SISO uncertain pure-feedback nonlinear systems with immeasurable states.Fuzzy logic systems are utilized to approximate the unknown nonlinear functions;and the filtered signals are introduced to circumvent algebraic loop systems encountered in the implementation of the controller,and a fuzzy state adaptive observer is designed to estimate the immeasurable states.By combining the adaptive backstepping technique,an adaptive fuzzy output feedback control scheme is developed.It is proven that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded(SGUUB),and the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Simulation studies are included to illustrate the efectiveness of the proposed approach.     

Observer-based fault tolerant control for a class of nonlinear multi-agent systems with sensor faults

This article focuses on the robust fault tolerant control (FTC) problem for a class of Lipschitz nonlinear multi-agent systems(MASs) subject to sensor faults. Firstly, sensor faults are transformed into actuator faults via introducing a new intermediate auxiliary state variable, and a distributed adaptive fault estimation observer is designed to estimate the state information and the concerned faults by using the relative output estimation error. Then, the sufficient existence conditions for the observer to satisfy the robust performance index are given. Thirdly, based on the results of observer design, a new design method of dynamic output feedback controller is proposed to implement consensus of MASs and ensure the desired disturbance rejection performance. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.     

Stable adaptive fuzzy control for MIMO nonlinear systems

In this paper, an indirect adaptive fuzzy control scheme is presented for a class of multi-input and multi-output (MIMO) nonlinear systems whose dynamics are poorly understood. Within this scheme, fuzzy systems are employed to approximate the plant’s unknown dynamics. In order to overcome the controller singularity problem, the estimated gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrices, a robustifying control term is used to compensate for the lumped errors, and all parameter adaptive laws and robustifying control term are derived based on Lyapunov stability analysis. The proposed scheme guarantees that all the signals in the resulting closed-loop system are uniformly ultimately bounded (UUB). Moreover, the tracking errors can be made small enough if the designed parameter is chosen to be sufficiently large. A simulation example is used to demonstrate the effectiveness of the proposed control scheme.     

基于观测器的非线性互连系统的自适应模糊控制

针对一类不确定非线性MIMO互连系统,提出一种自适应模糊控制算法.通过设计观测器来估计系统的状态,因此不要求假设系统的状态是可测的.给出的自适应律只对不确定界进行在线调节,从而大大减轻了在线计算负担.该算法能够保证闭环系统的所有信号是一致有界的,并且跟踪误差指数收敛到一个小的零邻域内.仿真结果表明了算法的可行性.     

Direct adaptive fuzzy control of a class of MIMO non-affine nonlinear systems

An adaptive fuzzy control approach is proposed for a class of multiple-input–multiple-output (MIMO) nonlinear systems with completely unknown non-affine functions. The global implicit function theorem is first used to prove the existence of an unknown ideal implicit controller that can achieve the control objectives. Within this scheme, fuzzy systems are employed the approximate the unknown ideal implicit controller, and robustifying control terms are used to compensate the approximation errors and external disturbances. The adjustable parameters of the used fuzzy systems are deduced from the stability analysis of the closed-loop system in the sense of Lyapunov. To show the efficiency of the proposed controllers, two simulation examples are presented.     

Observer-based adaptive fuzzy control for a class of nonlinear time-delay systems

An observer-based adaptive fuzzy control is presented for a class of nonlinear systems with unknown time delays. The state observer is first designed, and then the controller is designed via the adaptive fuzzy control method based on the observed states. Both the designed observer and controller are independent of time delays. Using an appropriate Lyapunov-Krasovskii functional, the uncertainty of the unknown time delay is compensated, and then the fuzzy logic system in Mamdani type is utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, the constructed observer-based controller and the closed-loop system are proved to be asymptotically stable. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.     

Event-triggered adaptive fuzzy tracking control of nonlinear MIMO systems

This paper addresses the problem of an adaptive fuzzy event-triggered control (ETC) for uncertain multi-input and multi-output nonlinear systems. To reduce the communication burden of the network control systems, a novel state-dependent event-triggering condition is designed to decide when to update the controllers. By combining the backstepping and event-trigged techniques, the adaptive fuzzy ETC strategies are developed and the resulting closed-loop system is semi-global bounded. Finally, the analytical results are substantiated using simulation studies.     

Approximation-based adaptive fuzzy tracking control for a class of switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy tracking control is investigated for switched nonlinear pure-feedback systems under arbitrary switching. By utilising mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Compared with the existing results, a priori knowledge of control directions is not required. On the other hand, differing from the existing literatures, the piecewise switched adaptive laws are designed to replace the common adaptive laws, which can reduce the conservativeness. Furthermore, the difficulties from how to deal with the unknown control directions and design common virtual control are overcome. Based on the backstepping technique and the common Lyapunov functions, an adaptive fuzzy control scheme is developed to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded with the tracking error converging to a neighbourhood of the origin. Simulation results are provided to demonstrate the effectiveness of the proposed techniques.     

Robust adaptive neural control for a class of uncertain MIMO nonlinear systems

In this paper, a novel robust adaptive neural control scheme is proposed for a class of uncertain multi-input multi-output nonlinear systems. The proposed scheme has the following main features: (1) a kind of Hurwitz condition is introduced to handle the state-dependent control gain matrix and some assumptions in existing schemes are relaxed; (2) by introducing a novel matrix normalisation technique, it is shown that all bound restrictions imposed on the control gain matrix in existing schemes can be removed; (3) the singularity problem is avoided without any extra effort, which makes the control law quite simple. Besides, with the aid of the minimal learning parameter technique, only one parameter needs to be updated online regardless of the system input–output dimension and the number of neural network nodes. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Adaptive fuzzy backstepping control for a class of switched nonlinear systems with actuator faults

This paper investigates the problem of fault-tolerant control (FTC) for a class of switched nonlinear systems. These systems are under arbitrary switchings and are subject to both lock-in-place and loss-of-effectiveness actuator faults. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. Under the framework of the backstepping control design, FTC, fuzzy adaptive control and common Lyapunov function stability theory, an adaptive fuzzy control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop switched system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error remains an adjustable neighbourhood of the origin. Two simulation examples are provided to illustrate the effectiveness of the proposed approach.     

Observer-based tracking control for MIMO pure-feedback nonlinear systems with time-delay and input quantisation

In addressing the adaptive neural backstepping control for multiple-input and multiple-output nonlinear systems in pure-feedback form with time-delay and input quantisation, we construct a high-gain state observer and an output-feedback adaptive control scheme using backstepping method, with neural networks to estimate the uncertain nonlinear functions. Then, we propose an output feedback neural controller that ensures all the state trajectories in the time-delay quantised nonlinear systems are ultimately bounded, with the control signal being quantised by either a hysteretic quantiser or a logarithmic quantiser. An illustrative example is presented to show the applicability of the new control method developed.     

基于观测器的不确定非线性系统的自适应鲁棒模糊控制

针对单输入单输出不确定非线性系统提出了一种自适应鲁棒模糊控制算法.该算法通过设计观测器来估计系统的状态向量,因此不要求假设系统的状态向量是可测的.在这个算法中,主要的假设为最优逼近参数向量与标称参数向量之差的范数和逼近误差的界限是未知的.通过只对未知界限估计的调节,该算法减轻了在线计算量并且提高了系统的鲁棒性.所设计的自适应鲁棒模糊控制算法保证了闭环系统的所有信号是一致有界的并且跟踪误差估计收敛到一个小的零邻域内.仿真例子证实了所提方法的可行性.     

Approximation-based adaptive fuzzy control for a class of non-strict-feedback stochastic nonlinear systems

This paper considers the problem of adaptive fuzzy control of a class of single-input/single-output （SISO） nonlinear stochastic systems in non-strict-feedback form. Fuzzy logic systems are used to approximate the uncertain nonlinearities and backstepping technique is utilized to construct an adaptive fuzzy controller. The proposed controller guarantees that all the signals in the resulting closed-loop system are bounded in probability. The main contribution of this note lies in providing a control strategy for a class of nonlinear systems in non- strict-feedback form. Simulation result is used to test the effectiveness of the suggested approach.     

Command filter-based adaptive fixed-time fault-tolerant control for stochastic nonlinear systems with actuator hysteresis

In this paper, an adaptive fault-tolerant fixed-time control problem is considered via command-filter technique for stochastic nonlinear systems with sensor fault and actuator hysteresis. With the application of command-filtering technique, a novel command-filter compensate mechanism is designed, which implies that the improved control scheme not only eliminates “the explosion of complexity” but also realizes the compensate signal is bounded within fixed-time interval. The unavailability of state variables caused by sensor fault is solved by applying parameter separation and regrouping approach. Meanwhile, an adaptive auxiliary signal is designed to cope with the backlash-like hysteresis phenomenon, which can avoid singularity, reduce chattering, and facilitate controller design. Combining backstepping technique and Lyapunov stability theorem, an adaptive fault-tolerant control approach is developed, which can guarantee all closed-loop signals remain semi-globally practical fixed-time stable (SGPFS) in probability. The validity of the proposed strategy is illustrated by simulation examples.     

一类MIMO非线性系统的直接自适应模糊滑模控制

针对一类具有下三角形函数控制增益矩阵的非线性系统, 基于滑模控制原理, 并利用Ⅱ型模糊系统的逼近能力, 提出了一种直接自适应模糊滑模控制器设计的新方案. 通过引入积分型李雅普诺夫函数及逼近误差自适应补偿项, 证明了闭环系统是全局稳定的, 跟踪误差收敛到零. 仿真结果表明了该方法的有效性.     

一类非线性时滞输出反馈系统的自适应控制

针对一类参数化非线性时滞输出反馈系统,提出了一种无记忆自适应跟踪控制器的设计方案.采用时滞滤波器估计系统状态,用Domination处理非线性时滞项,应用Backstepping技术设计控制器和参数自适应律.放宽了对时滞项的要求.通过构建一个Lyapunov＿Krasoviskii泛函,证明了闭环系统的稳定性,实现了对目标轨线的渐近跟踪,保证了所有信号一致有界.实例仿真说明了该方案的可行性.     

一类非线性MIMO系统的直接自适应模糊鲁棒控制

针对一类未知的非线性MIMO系统, 本文提出了一种直接自适应模糊鲁棒控制设计方法. 理论分析和仿真实验都已证明, 该方法确保闭环系统全局稳定, 获得H_∞跟踪性能指标, 外部干扰、模糊逻辑逼近误差和输入对输出的交叉耦合可衰减到给定的水平, 系统鲁棒性好.