不确定非线性环链系统的分散鲁棒控制

提出了环链系统和一类不确定非线性环链系统,利用线性代数理论,给出了实现环链系统的充要条件,运用李雅普诺夫稳定理论和矩阵理论研究了不确定非线性环链系统的鲁棒镇定,并给出了一种非线性鲁棒镇定控制器的设计,还考虑了一类非线性环链相似组合大系统,给出了分散鲁棒镇定条件,最后给出数值例子说明设计方法的有效性。     

基于模糊模型的非线性不确定时滞系统的H∞鲁棒容错控制

研究了一类具有不确定时滞的非线性系统的H∞鲁棒容错控制问题.采用T-S模糊模型来描述非线性系统,并对执行器失效且具有扰动的情形,基于Lyapunov稳定性理论和LMI方法,给出了系统H∞鲁棒容错控制器存在的充分条件,保证了系统的鲁棒稳定性.仿真实例验证了本文提出方法的有效性.     

基于Volterra泛函级数的非线性系统的鲁棒辨识

针对弱非线性系统的鲁棒建模问题, 基于Volterra泛函级数, 结合集员辨识理论, 提出了广义频率响应函数的鲁棒辨识方法, 形成了一套较完整的弱非线性系统的鲁棒建模方法, 仿真结果表明该方法是行之有效的.     

非线性不确定中立型系统的鲁棒H∞控制

考虑系统外界干扰、系统参数摄动等非线性扰动环节对中立型时滞系统的H∞影响,提出基于Lyapunov稳定性理论的鲁棒H∞控制器的设计思想.利用线性矩阵不等式(LMI)方法,给出了该类具有状态非线性不确定性中立型时滞系统的鲁棒∞控制器的设计实例.在非线性不确定函数满足增益有界的条件下,得到了该类时滞系统满足鲁棒∞性能的一个充分条件.通过求解一个线性矩阵不等式LMI,即可获得鲁棒∞控制器.仿真结果表明了基于Lyapunov稳定性理论,LMI技术设计的控制器克服了系统外界非线性干扰或系统本身非线性参数摄动的影响,实现了闭环系统的H∞性能条件下的渐近稳定,满足了该系统鲁棒H∞控制的要求.     

基于模糊T-S模型的非线性系统的H∞鲁棒容错控制

研究一类具有不确定和时滞的非线性系统的H鲁棒容错控制问题.采用T-S模糊模型来描述非线性系统,在系统执行器失效的情况下,建立故障矩阵模型;通过引进自由加权矩阵,基于Lyapunov稳定性理论和LMI(线性矩阵不等式)方法,给出系统H鲁棒容错控制器存在的充分条件,保证了系统的鲁棒稳定性,仿真实例验证了该方法的有效性.     

基于模糊模型的非线性不确定时滞系统的H-infinite鲁棒容错控制

研究了一类具有不确定时滞的非线性系统的H_∞鲁棒容错控制问题. 采用T-S模糊模型来描述非线性系统,并对执行器失效且具有扰动的情形, 基于Lyapunov稳定性理论和LMI方法, 给出了系统H_∞鲁棒容错控制器存在的充分条件, 保证了系统的鲁棒稳定性. 仿真实例验证了本文提出方法的有效性.     

非线性离散不确定系统的鲁棒H_∞状态反馈控制

研究具有不确定非线性离散系统的鲁棒性能准则问题 .基于二人零和动态对策理论 ,给出并证明了系统鲁棒稳定以及扰动衰减问题解存在的充分条件 ,通过求解离散时间Hamilton jacobi Isaacs方程给出了其鲁棒H∞ 状态反馈控制解 .     

非线性离散不确定系统的鲁棒H∞状态反馈控制

研究具有不确定非线性离散系统的鲁棒性能准则问题,基于二人零和动态对策理论,给出并证明了系统鲁棒稳定以及扰动衰减问题解存在的充分条件,通过求解离散时间Hamilton-jacobi-Isaacs方程给出了其鲁棒H∞状态反馈控制解。     

不确定非线性系统的鲁棒稳定性分析

基于泛函分析和算子理论的方法,从输入输出的角度研究了一类不确定反馈非线性系统的鲁棒稳定性问题.利用K类函数分别描述非线性不确定环节和非线性系统的算子增益,对非线性反馈互联不确定系统的鲁棒稳定性问题进行了研究.接着利用小增益条件的形式进行等价变化,就可将反馈不确定非线性系统的稳定性条件转化成系统非线性算子的范数条件.并通过举例证明了该方法的有效性.     

一类非线性广义系统的时滞相关耗散控制

针对一类带有非线性摄动的广义时滞系统,研究了时滞相关的鲁棒耗散问题.讨论了此类非线性广义时滞系统的鲁棒耗散性.同时对此类非线性广义时滞系统的二次稳定性进行了研究,分别用线性矩阵不等式（LMI）的方法给出了充分条件,也给出了时滞相关的鲁棒耗散的时滞上界.并且,给出了时滞相关的鲁棒耗散的状态反馈控制器.最后,通过例子验证了定理的可行性.     

Robust stabilization of nonlinear systems by H∞ state feedback

This paper is concerned with robust stabilization of nonlinear systems with unstructured uncertainty via state feedback. First, a robust stability condition is given for a closed loop system which is composed of a nonlinear nominal system and an unstructured uncertainty. Second, based on the obtained robust stability condition, a sufficient condition for robust stabilization by state feedback is given in terms of the solvability of some H_∞ state feedback control.     

Robust nonlinear ship course‐keeping control by H∞ I/O linearization and μ‐synthesis

In this paper, the H_∞ input/output (I/O) linearization formulation is applied to design an inner‐loop nonlinear controller for a nonlinear ship course‐keeping control problem. Due to the ship motion dynamics are non‐minimum phase, it is impossible to use the ordinary feedback I/O linearization to resolve. Hence, the technique of H_∞ I/O linearization is proposed to obtain a nonlinear H_∞ controller such that the compensated nonlinear system approximates the linear reference model in I/O behaviour. Then a μ‐synthesis method is employed to design an outer‐loop robust controller to address tracking, regulation, and robustness issues. The time responses of the tracking signals for the closed‐loop system reveal that the overall robust nonlinear controller is able to provide robust stability and robust performance for the plant uncertainties and state measurement errors. Copyright © 2002 John Wiley & Sons, Ltd.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust state feedback synthesis for control of non-square multivariable nonlinear systems

In this paper, a robust nonlinear controller is designed in the Input/Output (I/O) linearization framework, for non-square multivariable nonlinear systems that have more inputs than outputs and are subject to parametric uncertainty. A nonlinear state feedback is synthesized that approximately linearizes the system in an I/O sense by solving a convex optimization problem online. A robust controller is designed for the linear uncertain subsystem using a multi-model H₂/H_∞ synthesis approach to ensure robust stability and performance of non-square multivariable, nonlinear systems. This methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor.     

Robust H ∞ control of uncertain nonlinear switched systems using constructive method

This paper focuses on the problem of robust H _?? control of nonlinear switched systems with parameter uncertainty via the multiple Lyapunov functions (MLFs) approach. The uncertain parameters are assumed to be in a known compact set and are allowed to enter the system nonlinearly. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton-Jacobi-Isaacs (HJI) inequalities, sufficient conditions for the solvability of the robust H _?? control problem of cascade nonlinear switched systems are derived under some switching signal. Then, the result is extended to solve the robust H _?? control problem of nonlinear switched systems in strict feedback form. Finally, the effectiveness of the proposed results is illustrated through a simulation example.     

Nonlinear system modeling and robust predictive control based on RBF-ARX model

An integrated modeling and robust model predictive control (MPC) approach is proposed for a class of nonlinear systems with unknown steady state. First, the nonlinear system is identified off-line by RBF-ARX model possessing linear ARX model structure and state-dependent Gaussian RBF neural network type coefficients. On the basis of the RBF-ARX model, a combination of a local linearization model and a polytopic uncertain linear parameter-varying (LPV) model are built to approximate the present and the future system's nonlinear behavior, respectively. Subsequently, based on the approximate models, a min–max robust MPC algorithm with input constraint is designed for the output-tracking control of the nonlinear system with unknown steady state. The closed-loop stability of the MPC strategy is guaranteed by the use of parameter-dependent Lyapunov function and the feasibility of the linear matrix inequalities (LMIs). Simulation study to a NO_x decomposition process illustrates the effectiveness of the modeling and robust MPC approaches proposed in this paper.     

Coordinated nonlinear robust control of TCSC and excitation for multi-machine systems

An advanced nonlinear robust control scheme is proposed for multi-machine power systems equipped with thyristor-controlled series compensation (TCSC). First, a decentralized nonlinear robust control approach based on the feedback linearization and H∞ theory is introduced to eliminate the nonlinearities and interconnections of the studied system, and to attenuate the exogenous disturbances that enter the system. Then, a system model is built up, which has considered all the generators‘ and TCSC‘s dynamics, and the effects of uncertainties such as disturbances. Next, a decentralized nonlinear robust coordinated control law is developed based on this model. Simulation results on a six-machine power system show that the transient stability of the power system is obviously improved and the power transfer capacity of long distance transmission lines is enhanced regardless of fault locations and system operation points. In addition, the control law has engineering practicality since all the variables in the expression of he control strategy can be measured locally.     

NARX model based nonlinear dynamic system identification using low complexity neural networks and robust H∞ filter

This paper proposes NARX (nonlinear autoregressive model with exogenous input) model structures with functional expansion of input patterns by using low complexity ANN (artificial neural network) for nonlinear system identification. Chebyshev polynomials, Legendre polynomials, trigonometric expansions using sine and cosine functions as well as wavelet basis functions are used for the functional expansion of input patterns. The past input and output samples are modeled as a nonlinear NARX process and robust H_∞ filter is proposed as the learning algorithm for the neural network to identify the unknown plants. H_∞ filtering approach is based on the state space modeling of model parameters and evaluation of Jacobian matrices. This approach is the robustification of Kalman filter which exhibits robust characteristics and fast convergence properties. Comparison results for different nonlinear dynamic plants with forgetting factor recursive least square (FFRLS) and extended Kalman filter (EKF) algorithms demonstrate the effectiveness of the proposed approach.     

Guaranteed robustness bounds for matched-disturbance nonlinear systems

This paper considers input affine nonlinear systems with matched disturbances and shows how to compute an a priori upper bound of the H_∞ attenuation level achieved by the optimal L₂ controller and the suboptimal H_∞ central controller. The case where the disturbance contains a constant term is also discussed. These bounds are shown to depend only on the function mapping the control input to the performance variable. This result is used to derive a robust control design for a special, but practically important, class of non-input affine nonlinear systems consisting of the series connection of a nonlinear state and input dependent map and of a nonlinear input affine dynamical system. Approximate inversion of the nonlinear static map leads to a robust control problem which fits into the framework. The effectiveness of the theoretical results is shown by its use for the robust control design of a diesel engine test bench.