基于系统输出的嵌套饱和系统抗饱和补偿器设计

针对嵌套输入饱和系统的吸引域扩大问题,本文提出了一种基于系统输出的抗饱和补偿器激发策略,将被控系统输出信号经性能补偿器馈入到抗饱和补偿器激发环节中,形成蕴含系统实时性能信息的抗饱和激发新机制,克服了传统抗饱和激发机制无法直接反映系统性能的缺点.基于上述抗饱和控制新框架,本文建立了抗饱和补偿器及性能补偿器存在的充分条件,并依此构建了优化问题求解最优补偿器增益以实现扩大闭环系统吸引域的目的.仿真结果表明本文方法的有效性.     

Robust Stability and Stabilization of Positive Interval Systems Subject to Actuator Saturation

This paper addresses the stabilization problem for a class of uncertain positive linear systems (PLSs) in the presence of saturating actuators. The objective is to obtain sufficient conditions for the robust stability of PLSs and to design robust state feedback control laws such that the closed‐loop uncertain system is asymptotically stable and positive at the origin with a large domain of attraction. Several sufficient conditions for robust stabilization and positivity are derived via the Lyapunov function approach and convex analysis method for both the discrete‐time and the continuous‐time cases, respectively. The state feedback controller design and the estimation of the domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints. A numerical example is given to show the effectiveness of the proposed methods.     

含饱和状态反馈线性离散时间系统渐近稳定性

As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.     

On Asymptotic Stabilization of Linear Discrete-time Systems with Saturated State Feedback

As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.     

饱和约束控制系统的吸引域估计

饱和约束控制系统的吸引域估计是非线性系统领域的一个基本问题,主要涉及到饱和约束的处理和Lyapunov函数的选取.围绕这两个关键问题,梳理了解决饱和约束控制系统吸引域估计问题的一系列方法,总结了文献及最近的一些研究结果.     

Stability and stabilization of discrete-time periodic linear systems with actuator saturation

This paper is concerned with the problems of stability and stabilization for discrete-time periodic linear systems subject to input saturation. Both local results and global results are obtained. For local stability and stabilization, the so-called periodic invariant set is used to estimate the domain of attraction. The conditions for periodic invariance of an ellipsoid can be expressed as linear matrix inequalities (LMIs) which can be used for both enlarging the domain of attraction with a given controller and synthesizing controllers. The periodic enhancement technique is introduced to reduce the conservatism in the methods. As a by-product, less conservative results for controller analysis and design for discrete-time time-invariant systems with input saturation are obtained. For global stability, by utilizing the special properties of the saturation function, a saturation dependent periodic Lyapunov function is constructed to derive sufficient conditions for guaranteeing the global stability of the system. The corresponding conditions are expressed in the form of LMIs and can be efficiently solved. Several numerical and practical examples are given to illustrate the theoretical results proposed in the paper.     

Robust Control for a Class of Uncertain Switched Fuzzy Systems with Saturating Actuators

This paper investigates the robust control problem for a class of uncertain switched fuzzy systems with saturating actuators. The asymptotical stability for fuzzy subsystems subject to actuator saturation is not assumed. Based on the multiple Lyapunov functions method, we design a switching law and a state feedback control law such that the closed‐loop system is asymptotically stable. Additionally, the estimation of the domain of attraction is presented by solving an optimization problem. Finally, simulation results verify the feasibility and effectiveness of the proposed method.     

基于记忆型饱和控制器的非线性时滞系统的稳定性分析

针对在记忆型饱和控制器的作用下;研究非线性时滞系统的指数稳定性问题。首先;考虑系统参数不稳定的因素;其次;利用包含分布式时滞项辅助反馈的多面体方法处理饱和非线性;同时;建立增广Lyapunov-Krasovskii泛函;并利用改进的积分不等式放缩积分项;从而导出基于线性矩阵不等式（LMI）的稳定性准则;此外;制定保守性较低的吸引域优化方案;以提高吸引域的上界;最后;通过一个仿真实例证明所提方案的有效性和实用性。实验结果表明;在非线性系统中;在相同的参数条件下;与无记忆型控制器的现有的吸引域优化方案相比;所提有记忆型控制器的吸引域优化方案具有较低的保守性。     

运用线性反馈分析设计饱和线性系统

给出了状态反馈控制饱和单输入系统以及动态输出反馈单输出饱和线性系统是全局渐近稳定还是区域渐近稳定的充分性条件,并在区域渐近稳定的情况下计算其不变吸引椭球.对于控制饱和系统,运用Ricatti方程迭代法设计控制器,以使所得椭球尽量大.仿真算例说明了所提出方法的有效性.     

奇异线性系统在执行器饱和受限下不变集条件的改进(英文)

本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题.根据每个输入是否饱和,将输入空间分成若干子区域.在每个子区域内部,系统模型中没有显示的部分状态的时间导数可被显式表达.利用含有全部系统状态的二次Lyapunov函数,建立一组双线性矩阵不等式形式的改进的不变集条件.该组条件下,二次Lyapunov函数的水平集可诱导出一个吸引域估计.为得到最大的吸引域估计,构建了以这些双线性矩阵不等式为约束条件的优化问题,并为其求解给出了迭代算法.仿真结果表明本文得到的吸引域估计明显大于现有结果.     

Observer-based direct adaptive fuzzy control of uncertain nonlinear systems and its applications

A direct adaptive fuzzy control algorithm is developed for a class of uncertain SISO nonlinear systems. In this algorithm, it doesn’t require to assume that the system states are measurable. Therefore, it is needed to design an observer to estimate the system states. Compared with the numerous alternative approaches with respect to the observer design, the main advantage of the developed algorithm is that on-line computation burden is alleviated. It is proven that the developed algorithm can guarantee that all the signals in the closed-loop system are uniformly ultimately bounded and the tracking error converges to a small neighborhood around zero. The simulation examples validate the feasibility of the developed algorithm. Recommended by Editorial Board member Zhong Li under the direction of Editor Young-Hoon Joo. This work is supported by National Natural Science Foundation of China under grant 60674056, 60874056, and the Foundation of Educational Department of Liaoning Province (2008312). Yan-Jun Liu received the B.S. degree in Applied Mathematics from Shenyang University of Technology in 2001. He received the M.S. degree in Control Theory and Control Engineering from Shenyang University of Technology in 2004 and the Ph.D. degree in Control Theory and Control Engineering from Dalian University of Technology, China, in 2007. His research interests include fuzzy control theory, nonlinear control and adaptive control. Shao-Cheng Tong received the B.S. degree in Department of Mathematics from Jinzhou Normal College, China, in 1982. He received the M.S. degree in Department of Mathematics from Dalian Marine University in 1988 and the Ph.D. degree in Control Theory and Control Engineering from Northeastern University, China, in 1997. His research interests include fuzzy control theory, nonlinear control, adaptive control, and system identification etc. Wei Wang received the B.S. degree in Department of Automation from Northeastern University, China, in 1982. He received the M. S. degree in Department of Automation from Northeastern University in 1984 and the Ph.D. degree in Department of Automation from Northeastern University, China, in 1988. His research interests include adaptive predictive control, intelligent control, and production scheduling method etc. Yong-Ming Li received the B.S. degree in Applied Mathematics from Liaoning University of Technology in 2004. He received the M.S. degree in Applied Mathematics from Liaoning University of Technology in 2007. His research interests include fuzzy control theory, nonlinear control and adaptive control.