传感器失效下不确定离散时滞系统的静态输出反馈鲁棒可靠保成本控制

针对一类参数不确定离散时滞系统,研究了当传感器发生增益故障情况下的静态输出反馈保成本可靠控制器设计问题.系统中的参数不确定性满足广义匹配条件,传感器元件具有部分输出增益故障.根据Lyapunov稳定性理论和线性矩阵不等式(LMI)方法,分别给出了含有时滞记忆和无时滞静态输出反馈保成本鲁棒可靠控制律的存在条件.通过求解由一组线性矩阵不等式所表示的凸优化问题可以得到使得闭环保成本上界最小的鲁棒可靠控制器.最后通过仿真示例说明所提出方法的正确性.     

一类不确定性时滞关联大系统的分散鲁棒稳定控制器设计

对一类满足匹配条件的不确定性关联大系统，设计了基于一组线性矩阵不等式（LMI）有解的系统状态反馈镇定的充分条件。本文采用了实对称矩阵集合的最小上界定理，并对设计参数进行优化处理，从而使得所设计的控制器具有较小反馈增益。同时系统的不确定性采用区间矩阵表示，因此该设计方法具有很好的普遍性。最后给出的仿真实例说明了该方法的有效性。     

一类不确定非线性时滞系统的可靠保成本控制

针对包含时滞的一类非线性不确定系统,在执行器可能发生故障的情况下,研究了此类系统可靠控制器的设计和成本上界的确定问题。从Lyapunov定理出发,经演绎后得到可靠控制器和成本有界需要满足的矩阵不等式,通过利用Schur补定理,将矩阵不等式化为标准的LMI,同时给出了系统控制器和成本上界。闭环控制器能够使得系统在执行器失效时系统对允许的不确定性具有容错能力,且保成本上界的存在。最后通过给出一个系统实例,检验了所提出方法的可应用性。     

结构不确定离散系统的最优非脆弱保成本控制

讨论了一类不确定线性离散系统的最优非脆弱保成本控制问题.考虑的系统和状态反馈控制器均具有时变的结构化的不确定性.基于线性矩阵不等式的方法,给出了存在和设计非脆弱保成本控制律的一个充分条件,以及在使二次成本函数上界最小意义下,最优非脆弱保成本控制律的凸优化设计方法.并用数值例子说明该方法降低了成本函数上界的保守性.     

基于观测器的广义时滞系统弹性保成本控制

在同时考虑系统矩阵参数不确定性和控制器不确定性对系统性能影响的前提下,研究了一类基于观测器的不确定广义时滞系统的弹性保成本控制问题.基于Lvapunov稳定性理论,通过构造广义Lyapunov函数和广义二次性能指标函数,以线性矩阵不等式的形式给出了基于观测器状态反馈的弹性保成本控制器的设计方法.该控制器不仅保证了广义时滞系统是鲁棒稳定而且使其具有相应的性能指标上界.采用一种新方法将系统弹性保成本控制器设计和状态观测器增益矩阵求取转化为两组严格线性矩阵不等式的可行解问题.最后通过算例验证了该方法的可行性和有效性.     

时变不确定多时滞连续系统的最优保成本控制

针对一类同时具有状态多时滞和输入多时滞的时变不确定连续多时滞系统。研究保成本状态反馈控制器的设计。假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件,通过构造改造的Lyapunov函数和线性矩阵不等式（LMI）方法,给出系统满足保性能指标的一个充分条件,仅通过求解一个相应的线性矩阵不等式,就可得到保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界。通过求解凸优化问题得到最优保性能控制器,最后用数值例子说明该方法的有效性。     

一类关联不确定离散系统的分散保性能控制

结合一个给定的二次型性能指标, 研究一类关联不确定离散大系统的分散保性能状态反馈控制器设计问题. 采用线性矩阵不等式处理方法, 导出了分散控制器存在的条件, 并给出了一组分散保性能控制器的参数化表示, 据此, 通过建立和求解一个凸优化问题给出了使得闭环性能指标的上界最小化的最优分散保性能控制器设计方法.     

具有H∞干扰抑制的中立型系统保成本控制

针对一类范数有界时变非线性不确定性的中立型系统,将其转化为时滞广义系统.利用时滞广义系统的相关理论、Lyapunov-Krasovskii稳定性定理和线性矩阵不等式方法,通过无记忆状态反馈实现了具有H∞干扰抑制的保成本控制,并给出了具有H∞干扰抑制的中立型系统保成本控制器存在的充分条件及相应的干扰抑制保成本指标.控制器的设计使得闭环系统鲁棒稳定,具有给定H∞干扰衰减度同时使给定的干扰抑制保成本指标最优.所得结论等价于一组线性矩阵不等式（LMI）的可解性问题.最后给出算例以验证设计方法的有效性.     

线性分式不确定系统保成本控制及其鲁棒界

研究线性分式不确定系统的动态输出反馈保成本控制.采用线性矩阵不等式(LMI)方法证明了保成本控制器存在的充分必要条件等价于一个LMI可解性问题,通过该条件将求解闭环系统的成本函数上界的最小值问题转化为一个凸优化问题,利用该凸优化问题的解,得到动态输出反馈控制器的增益矩阵,并且给出了摄动参数允许最大摄动界的一种算法.     

不确定离散系统的输出反馈保性能控制

对一类具有范数有界时变参数不确定性的离散时间系统，研究设计一个输出反馈保性能控制器，使得闭环系统对所有允许的不确定性渐近稳定，且闭环性能指标值不超过某个确定的上界。基于线性矩阵不等式处理方法，证明了保性能控制器的存在性等价于一个线性矩阵不等式的可行性，并用该线性矩阵不等式的可解给出了控制器的构造方法和闭环性能指标的上界。     

An LMI approach to guaranteed cost control for uncertain linear neutral delay systems

This paper considers the problem of guaranteed cost control for uncertain neutral delay systems with a quadratic cost function. The system under consideration is subject to norm‐bounded time‐varying parametric uncertainty appearing in all the matrices of the state‐space model. The problem we address is the design of a state feedback controller such that the closed‐loop system is not only stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is given in terms of a linear matrix inequality (LMI). When this condition is feasible, the desired state feedback controller gain matrices can be obtained via convex optimization. An illustrative example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2002 John Wiley & Sons, Ltd.     

指数稳定的机器人鲁棒跟踪控制

本文提出了一种用于控制具有参数不确性机器人轨迹踊跃的鲁棒控制策略，该控制器的设计根据Ｌｙａｐｕｎｏｖ理论，由一个基于Ｓｌｏｔｉｎｅ方法的标称控制器和一个非线性连续反馈补偿器组成。     

Optimal adaptive design of the prescribed-structure controllers

For the continuous linear control plants with parametric uncertainty, a new approach to the H₂-design of multivariable controllers of the prescribed structure was suggested. For the desired reference model of the control system of full and low order, the property of adaptability of such control systems was defined, and the criteria for adaptability in terms of matrices and adaptability gramians were formulated. The structural properties of the matrices and adaptability gramians were analyzed, and their relation to the matrices and the gramians of controllability and observability were established. A new approach to the parametric controller optimization with the use of adaptability gramians was proposed. The integral estimates of the degree of deviation of the performance indices of the stationary continuous control systems with a prescribed-structure controller and the parametric uncertainty of the interval-type plant from the performance indices of the desired reference model of full and low order were obtained.     

参数不确定离散广义大系统的保性能控制

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper. The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model. The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities (LMIs), and a desired state feedback controller is obtained via convex optimization. An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

Guaranteed Cost Control for Discrete-time Singular Large-scale Systems with Parameter Uncertainty

The problem of optimal guaranteed cost control for discrete-time singular large-scale systems with a quadratic cost function is considered in this paper.The system under discussion is subject to norm bounded time-invariant parameter uncertainty in all the matrices of model.The problem we address is to design a state feedback controller such that the closed-loop system not only is robustly stable but also guarantees an adequate level of performance for all admissible uncer- tainties.A sufficient condition for the existence of guaranteed cost controllers is presented in terms of linear matrix inequalities(LMIs),and a desired state feedback controller is obtained via con- vex optimization.An illustrative example is given to demonstrate the effectiveness of the proposed approach.     

A new design of robust filters for uncertain systems

In this paper, a structured polynomial parameter-dependent approach is proposed for robust H₂ filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with s vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust H₂ filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of s matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples.     

不确定线性时滞系统的一种混杂状态反馈保成本控制及优化设计方法

本文研究一类不确定线性时滞系统的混杂状态反馈保成本控制及优化设计问题.假设存在有限个备选的控制增益已知的控制器,并且其中任何单一的状态反馈控制器都不能镇定系统,基于单Lyapunov函数的方法,给出了混杂状态反馈保成本控制的充分条件及优化设计方案.当备选的控制增益未知时,利用多Lyapunov函数法,同样给出混杂状态反馈保成本控制的充分条件及相应的优化设计方法.最后用仿真验证了文中方法的有效性.     

不确定线性系统保代价控制的鲁棒性分析

研究不确定线性系统保代价控制的鲁棒性分析问题.提出了不确定线性系统保代价 控制鲁棒界概念,给出了不确定线性系统保代价控制的一种鲁棒性分析方法,并建立了不确 定线性系统的参数可变保代价控制鲁棒界.针对一类结构不确定线性系统,进一步给出了保 代价控制鲁棒界的一种优化算法,并用实例加以验证.