Robust Tracking and Model Following Control with Zero Tracking Error for Uncertain Dynamical Systems

The problem of robust tracking and model following for a class of linear dynamical systems with time-varying uncertain parameters and disturbances is considered. A class of continuous (nonlinear) state feedback controllers is proposed for robust tracking of dynamical signals. The proposed robust tracking controllers can guarantee that the tracking error decreases asymptotically to zero in the presence of uncertain parameters and disturbances. A procedure for designing such a zero tracking state feedback controller is also introduced. Finally, a numerical example is given to demonstrate the validity of the results.     

Hilbert空间线性二次最优控制问题中的一个算子的可逆性

对于如下出现在Hilbert空间线性二次最优控制问题中的线性算子■其中F_3,F_5是自伴算子．本文得到了它具有有界逆的充分必要条件,并举例验证了结果的有效性．     

Output Feedback Guaranteed Cost Control for Uncertain Discrete-Time Systems Using Linear Matrix Inequalities

This paper considers the output feedback guaranteed cost controller design problem for uncertain discrete-time systems. The uncertainty is assumed to be of linear fractional form, unstructured, and is allowed to be time-varying. It is proved that the existence of a guaranteed cost controller is equivalent to the feasibility of a certain linear matrix inequality (LMI), and that a full-order output feedback controller can be constructed in terms of the feasible solution to the LMI. Furthermore, a convex optimization problem is introduced for the selection of a suitable controller minimizing a specified cost bound.     

Guaranteed Cost Control of a Markov Jump Linear Uncertain System Using a Time-Multiplied Cost Function

This paper addresses the guaranteed cost control problem of jump linear systems with norm-bounded uncertain parameters. A time-multiplied performance index is considered. The performance is calculated first and an LMI-based algorithm is developed to design a state feedback control law with constant gain matrices which robustly stabilizes the system in the mean-square quadratically stable sense.     

Decentralized Robust Tracking and Model Following for Uncertain Large-Scale Interconnected Systems

The problem of the decentralized robust tracking and model following is considered for a class of large-scale interconnected systems with uncertainties. A class of continuous (nonlinear) decentralized state feedback controllers is proposed. The proposed robust decentralized controllers can guarantee that the tracking errors between each subsystem and the local reference model decrease to zero asymptotically. Finally, an illustrative example is given to demonstrate the validity of the results.     

Minimax Control for a Class of Linear Systems Subject to Disturbances<Superscript>1</Superscript>

A class of linear dynamical control systems subject to uncertain but bounded disturbances is considered. The bounds imposed on the disturbances depend on the control magnitude and grow with the control. This situation occurs if the disturbances are due to the inaccuracy of the control implementation and often takes place in engineering applications such as transportation, aerospace, and robotic systems. Under certain assumptions, the minimax control problem is formulated and solved. Explicit expressions for the optimal control (both open-loop and feedback) are obtained that provide the minimax to the given performance index for arbitrary but bounded disturbances. Examples are given. ¹This work was supported by the Russian Foundation for Basic Research (Project 05-01-00647) and the Grant for Russian Scientific Schools (NSh 1627.2003.1).     

Robust control design for a class of mismatched uncertain nonlinear systems

We consider the robust control design problem for a class of nonlinear uncertain systems. The uncertainty in the system may be due to parameter variations and/or nonlinearity. It may be possibly fast, time-varying. The system does not satisfy the so-called matching condition. Under a state transformation, which is based on the possible bound of the uncertainty, a robust control scheme can be designed. The control renders the original uncertain system practically stable. Furthermore, the uniform ultimate boundedness ball and uniform stability ball of the original system can be made arbitrarily small by suitable choice of design parameters.     

Receding-Horizon Control Method for the Stabilization of an Unpredictably Changing Discrete-Time Uncertain System

The paper is concerned with the applicability of the receding-horizon control method for stabilizing a discrete-time uncertain system with a time-varying linear nominal part. The specific feature of the problem is that the nominal system is supposed to be known only up to the actual time. The effectiveness of the method is illustrated by an example.     

一类不确定双线性系统的状态反馈Robust控制*

本文针对一类含不确定性的双线性系统设计了一种线性状态反馈控制.在一定的条件下,利用改进的李雅普诺夫第二方法关于稳定性的理论,证明了系统的稳定性.并给出例子说明.     

Optimal Control of Linear Time-Varying Systems via Haar Wavelets

This paper introduces the application of Haar wavelets to the optimal control synthesis for linear time-varying systems. Based upon some useful properties of Haar wavelets, a special product matrix, a related coefficient matrix, and an operational matrix of backward integration are proposed to solve the adjoint equation of optimization. The results obtained by the proposed Haar approach are almost the same as those obtained by the conventional Riccati method.     

LMI Approach to Output Feedback Control for Linear Uncertain Systems with D-Stability Constraints

This paper deals with the problem of designing output feedback controllers for linear uncertain continuous-time and discrete-time systems with circular pole constraints. The uncertainty is assumed to be norm bounded and enters into both the system state and input matrices. We focus on the design of a dynamic output feedback controller that, for all admissible parameter uncertainties, assigns all the closed-loop poles inside a specified disk. It is shown that the problem addressed can be recast as a convex optimization problem characterized by linear matrix inequalities (LMI); therefore, an LMI approach is developed to derive the necessary and sufficient conditions for the existence of all desired dynamic output feedback controllers that achieve the specified circular pole constraints. An effective design procedure for the expected controllers is also presented. Finally, a numerical example is provided to show the usefulness and applicability of the present approach.     

线性系统最优输出转移问题的反馈解

在适当的条件下讨论如何最佳地施加控制将系统的输出转移至目标点,用来度量控制优劣的指标综合反映了转移时间,转移过程所消耗的输入能量与系统自身运动过程所具有的能量的多少,给出了使此指标达到最小的(状态)反馈控制．     

Solutions for the Linear-Quadratic Control Problem of Markov Jump Linear Systems

The paper is concerned with recursive methods for obtaining the stabilizing solution of coupled algebraic Riccati equations arising in the linear-quadratic control of Markovian jump linear systems by solving at each iteration uncoupled algebraic Riccati equations. It is shown that the new updates carried out at each iteration represent approximations of the original control problem by control problems with receding horizon, for which some sequences of stopping times define the terminal time. Under this approach, unlike previous results, no initialization conditions are required to guarantee the convergence of the algorithms. The methods can be ordered in terms of number of iterations to reach convergence, and comparisons with existing methods in the current literature are also presented. Also, we extend and generalize current results in the literature for the existence of the mean-square stabilizing solution of coupled algebraic Riccati equations.     

一类切换线性系统的动态输出反馈H_∞控制:LMIs方法

研究一类由任意有限多个线性子系统组成的切换系统的动态输出反馈H∞控制问题.利用共同Lyapunov函数方法和凸组合技术,给出由矩阵不等式表示的控制器存在的充分条件,并设计了相应的子控制器和切换规则.采用消元法,将该矩阵不等式转化为一组线性矩阵不等式(LMIs).最后给出一个数值仿真实例证明结论的有效性.     

一类不确定混沌系统的自适应跟踪控制

对一类不确定混沌系统 ,讨论了系统的自适应跟踪控制问题 .基于 Lyapunov函数方法 ,构造出了一类新的自适应控制器 .该控制器的构造简单 ,并能控制着混沌系统的状态全局渐近跟踪预先给定的任何有界轨线 .仿真实例验证了所得控制器的有效性 .     

基于LMIs的一类不确定线性切换系统的鲁棒控制

基于LMIs处理方法,研究了一类不确定线性切换系统在任意切换下的鲁棒控制问题.利用矩阵Schur补引理构造线性矩阵不等式,得到该系统的鲁棒稳定性的充要条件,同时也给出了在状态反馈下的鲁棒稳定性充要条件和在输出反馈下的充分条件.最后用数值例子对所得结果加以验证,说明了文中结果的正确性.     

基于输出反馈的一类大型互联非线性系统的鲁棒全局指数稳定

研究基于输出反馈的一类新的大型互联非线性不确定系统的鲁棒全局指数稳定问题,通过构造每个子系统收敛的状态观测器,并对观测器的状态作线性变换,得到鲁棒分散输出反馈控制器.当该反馈控制律作用于该系统时,闭环系统是全局指数稳定的.     

State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets

The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.     

一类不确定非线性系统的适应H-infinity控制

主要讨论了一类具有不确定参数的非线性系统的通过适应输出反馈达到干扰衰减的问题．通过构造降维观测器,利用Backstepping方法设计输出反馈控制器,使闭环系统具有不确定参数的标准的增益问题可解,并使系统达到内稳定．     

Relaxed LMI Condition for Output Feedback Guaranteed Cost Control of Uncertain Discrete-Time Systems

This paper studies the output feedback guaranteed cost control for a class of uncertain discrete-time systems. The uncertainty is of the linear fractional form. A new relaxed LMI condition is given based on a recently developed stability condition. An extra variable is introduced to obtain a less conservative result. The effectiveness of the method is illustrated with an example to compare with previous results. This work was supported in part by the National Science Foundation of China, Grant 10472001.