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.     

Stable nonlinear controller design for a Takagi-Sugeno fuzzy model

This paper proposes another adaptive control scheme for nonlinear systems using a Takagi-Sugeno fuzzy model. Takagi-Sugeno fuzzy models have been widely used to identify the structures and parameters of unknown or partially known plants, and to control nonlinear systems. This scheme shows a good approximation capability by the fuzzy blending of local dynamics. Since a Takagi-Sugeno fuzzy model is a nonlinear system in nature, and its parameters are not linearly parameterized, it is difficult to design an adaptive controller using conventional design methods for adaptive controllers which are derived from linearly parameterized systems. In this paper, the functional form of the local dynamics are assumed to be known, but the corresponding parameters are unknown. This additional information about system nonlinearity makes it possible to design an adaptive controller for a nonlinearly parameterized system. The control law is similar to that of a conventional adaptive control technique, while its parameter-update rule is based on the local search method. A parameter-update law is derived so that the time-derivative of the Lyapunov function is negative in the region of interest. Simulation results have shown that this adaptive controller is capable of a good performance. This work was presented in part at the Fifth International Symposium on Artificial Life and Robotics, Oita, Japan, January 26–28, 2000     

Robust adaptive tracking control for a class of switched time-delay systems with application of vehicle roll dynamic control

The problems of stability and robust tracking control for a class of switched nonlinear systems with uncertain input and state delays are investigated in this study. In the presence of unknown functions and external disturbances, an adaptive fuzzy technique based on nonlinear disturbance observer is used to counteract the effects of external disturbances and approximate unknown functions. For this purpose, it is first assumed that a common Lyapunov function exists for the switched system, and then a new common Lyapunov–Krasovskii functional is built using the terms of the hypothetical common Lyapunov function. By employing this new function, the delay-dependent input-to-state stability (ISS) under an arbitrary switching signal is provided. The robust tracking control problem for this system is investigated next. Finally, to assure ISS and robust tracking performance, an adaptive control law is developed that ensures conditions of the aforementioned hypothetical common Lyapunov function. In addition, to demonstrate the efficiency of the proposed strategy, the aforesaid method is applied to a vehicle roll dynamic as well as a mass-spring system.     

一类非线性系统的间接自适应模糊滑模控制

基于启发式知识的模糊控制是一种解决非线性系统控制问题的有效方法。然而其设计缺乏系统性,并且系统的稳定性和鲁棒性难以保证。本文利用滑模控制的概念和Lyapunov综合方法提出一种针对一类非线性系统的间接自适应模糊滑模控制（IAFSMC）方法。仿真研究表明即使在缺少系统先验知识和不确定性干扰的情况下,系统性能也十分理想。     

控制方向未知的SISO非仿射系统间接自适应模糊输出反馈控制

针对一类单输入单输出(SISO)非仿射非线性系统控制方向未知时出现的控制器奇异问题,提出了一种间接自适应模糊控制方案.利用中值定理将非仿射系统转化为仿射系统,通过模糊逻辑系统逼近该仿射系统中的未知函数,并构造模糊控制器,同时利用Lyapunov稳定性定理设计自适应律,最终克服了控制器的奇异问题;在此基础上,通过构造观测器估计跟踪误差,设计输出反馈自适应模糊控制器,解决了状态不可测时系统控制器设计难题,采用Lyapunov稳定性定理证明控制器能使得跟踪误差收敛同时闭环系统所有信号均有界.仿真结果验证了所设计控制方案的可行性与有效性.     

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.     

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT

This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.     

Adaptive fuzzy semi‐decentralized control for a class of large‐scale nonlinear systems with unknown interconnections

In this paper, a general method is developed to generate a stable adaptive fuzzy semi‐decentralized control for a class of large‐scale interconnected nonlinear systems with unknown nonlinear subsystems and unknown nonlinear interconnections. In the developed control algorithms, fuzzy logic systems, using fuzzy basis functions (FBF), are employed to approximate the unknown subsystems and interconnection functions without imposing any constraints or assumptions about the interconnections. The proposed controller consists of primary and auxiliary parts, where both direct and indirect adaptive approaches for the primary control part are aiming to maintain the closed‐loop stability, whereas the auxiliary control part is designed to attenuate the fuzzy approximation errors. By using Lyapunov stability method, the proposed semi‐decentralized adaptive fuzzy control system is proved to be globally stable, with converging tracking errors to a desired performance. Simulation examples are presented to illustrate the effectiveness of the proposed controller. Copyright © 2006 John Wiley & Sons, Ltd.     

利用模糊系统的直升机的自适应控制

针对直升机动力学为非线性,且存在不确定因素和状态变化,设计利用模糊系统的自适应控制器.设计的控制器是系统的输出跟踪参考模型输出的直接调整模糊控制器参数的自适应控制器.又利用Lyapunov函数保证了闭环控制系统的稳定性并推导最优的自适应规律.实验结果表明,有外部扰动的情况下所设计的自适应控制器比模糊控制器对直升机控制具有良好的动态响应和稳定性,是一种非常有效的控制方法.     

具有预设性能的切换系统输出反馈自适应动态面控制

本文针对一类具有未建模动态和预设性能的输出反馈非线性切换系统,提出基于公共Lyapunov函数法的自适应输出反馈动态面控制方案.通过设计K滤波器和观测器估计不可测量的状态.引入动态信号处理动态不确定性.利用Nussbaum函数解决增益符号未知的问题.神经网络用于逼近由设计过程和理论分析所产生的未知连续函数.引入性能函数和误差转换器将预设性能控制问题转换为稳定性问题.通过适当选取切换子系统的初值,并利用动态面控制系统证明的特点,证明了闭环切换系统所有信号半全局一致终结有界.仿真例子验证了所提方案的有效性.     

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.     

Asymptotic tracking control for constrained nonstrict‐feedback MIMO nonlinear systems via parameter compensations

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.     

An adaptive fuzzy controller based on sliding mode for robotmanipulators

This paper considers adaptive fuzzy control of robotic manipulators based on sliding mode. It is first shown that an adaptive fuzzy system with the system representative point (RP, or as is often termed, a switching function in variable structure control (VSC) theory) and its derivative as inputs, can approximate the robot nonlinear dynamics in the neighborhood of the switching hyperplane. Then a new method for designing an adaptive fuzzy control system based on sliding mode is proposed for the trajectory tracking control of a robot with unknown nonlinear dynamics. The system stability and tracking error convergence are also proved by Lyapunov techniques.     

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.     

一类多变量非线性动态系统的模糊自适应控制

对一类非线性多变量未知动态系统，提出了一种模糊处在适应控制策略。证明了该控制算法能保证闭环系统稳定，跟踪误差收敛。     

基于观测器的网络切换模糊时滞系统鲁棒控制

针对带有随机时变时滞的非线性网络切换系统稳定控制问题进行研究,在系统状态不可测且存在不确定性的情况下,采用T-S模型将非线性网络切换系统建模为网络切换模糊系统。然后,采用平均驻留时间法（ADT）,设计出基于观测器的控制器及系统切换律,并给出网络切换模糊系统指数稳定的平均驻留时间条件。结合李雅普诺夫（LKF）方法给出时滞相关的网络切换模糊系统指数稳定的矩阵不等式条件。最后通过MATLAB数值仿真验证了该设计方法的有效性和优越性。     

Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators

A stable decentralized adaptive fuzzy sliding mode control scheme is proposed for reconfigurable modular manipulators to satisfy the concept of modular software. For the development of the decentralized control, the dynamics of reconfigurable modular manipulators is represented as a set of interconnected subsystems. A first‐order Takagi–Sugeno fuzzy logic system is introduced to approximate the unknown dynamics of subsystem by using adaptive algorithm. The effect of interconnection term and fuzzy approximation error is removed by employing an adaptive sliding mode controller. All adaptive algorithms in the subsystem controller are derived from the sense of Lyapunov stability analysis, so that resulting closed‐loop system is stable and the trajectory tracking performance is guaranteed. The simulation results are presented to show the effectiveness of the proposed decentralized control scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

考虑输入约束的发电机汽门非线性自适应控制

研究具有汽门控制和阻尼系数不确定的单机无穷大系统的暂态稳定性问题. 通过引入切换机制, 解决了输入控制量幅值约束问题. 基于主汽门控制和快速汽门控制思想, 建立了一个由汽门控制的单机无穷大汽轮发电机切换系统模型. 应用本文提出的改进自适应Backstepping方法设计了切换子系统的非线性自适应控制器和参数替换律, 同时构造出切换系统的共同Lyapunov函数, 从而保证了切换系统的稳定性. 由于设计过程中, 未用到任何线性化方法, 因而所得控制器充分利用了系统的非线性特性. 仿真结果表明了设计方法的有效性和优越性.     

机械手的神经网络稳定自适应控制

本文针对机械手轨迹跟随控制问题，提出了一种稳定的神经网络自适应控制器设计方法，这里机械的非线性动力学假设是未知的，提出方法是神经网络方法和扇区自适应变结构控制方法的集成，扇区变结构控制的作用有两个，其一是在系统神经网络控制失灵的情形下提供闭环系统的全局稳定性；其二是在神经网络的近似域内改进系统的跟随性能，本文采用李雅普诺夫稳定理论给出了的稳定性和跟随误差收敛性的证明，并且通过数字仿真验证了提出方法     

Adaptive finite-time consensus in multi-agent networks

This paper is concerned with the finite-time consensus problem of distributed agents having non-identical unknown nonlinear dynamics, to a leader agent that also has unknown nonlinear control input signal. By parameterization of unknown nonlinear dynamics, a Lyapunov technique in conjunction with homogeneity technique is presented for designing a decentralized adaptive finite-time consensus control protocol in undirected networks. Homogeneous Lyapunov functions and homogeneous vector fields are introduced in the stability analysis although the whole system is not homogeneous. Theoretical analysis shows that leader-following consensus can be achieved in finite-time, meanwhile, finite-time parameter convergence can be also guaranteed under the proposed control scheme. An example is given to validate the theoretical results.