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.     

基于观测器具有不确定性的鲁棒保性能控制

在鲁棒性控制问题的研究中,针对系统状态不可测的具有范数有界不确定性和外界干扰的线性系统,其求解过程繁琐,某些参数选取不当.为了保证闭环系统的稳定性,提出一种基于观测器的鲁棒 H∞保性能控制方法.根据李亚普诺夫原理和H∞理论,获得鲁棒H∞保性能控制器存在的一个充分性条件,用矩阵奇异值分解方法,将控制器和观测器存在条件转化为求解一个线性矩阵不等式的可行性.通过凸优化方法,获得最优的线性二次型性能指标和 H∞性能指标.进行仿真的结果表明,上述方法求解简单,稳定性好,验证了所提方法的有效性.     

基于随机鲁棒设计的高超音速飞行器线性二次型控制

针对高超音速飞行器具有高度非线性、输入输出之间强耦合以及参数不确定等特点,提出了基于随机鲁棒设计的线性二次型控制。这一控制方案基于系统控制需求,利用蒙特卡罗仿真方法建立随机鲁棒目标函数,并通过遗传算法优化控制系统设计参数。该控制方案保证了飞行的纵向稳定性,改善了其控制性能。基于某常规高超音速飞行器纵向模型进行仿真验证,结果表明该方案能够满足系统控制需求且具有强鲁棒性。     

不确定广义大系统分散鲁棒H∞保性能控制

针对一类状态矩阵和控制矩阵存在参数不确定的广义大系统,研究其分散鲁棒H∞保性能控制问题,系统中不确定项具有数值界,可不满足匹配条件.基于广义系统的有界实引理,应用线性矩阵不等式(LMI)方法,给出了不确定广义大系统存在分散鲁棒H∞保件能控制器的一个LMI条件,并用这个线性矩阵不等式系统的可行解提供了一组分散鲁棒H∞保性能控制律的参数化表示,最后用例子说明该方法的应用.     

不确定离散切换系统具有极点约束的保性能控制

对一类含有范数有界不确定性的离散切换系统和一个二次型性能指标，研究其具有闭环极点约束的鲁棒状态反馈保性能控制问题．利用二次Lyapunov函数方法和线性矩阵不等式技术，给出了鲁棒保性能控制器存在的一个充分条件，在所构造切换规则下，闭环系统二次D稳定，且满足给定的性能指标．在此基础上，将次优保性能控制器设计问题转化为一组线性矩阵不等式约束下的凸优化问题．数值例子说明了所提方法的有效性．     

不稳定时滞对象的最优鲁棒二自由度控制器解析设计

针对不稳定时滞对象提出一种二自由度控制器解析设计方法．通过内模控制规律进行控制器设计,改进内模控制的滤波器提高系统的鲁棒性及其性能．同时对系统的稳定性、鲁棒性及性能进行分析,提出了严格基于模型信息的鲁棒指标选择规则,保证系统获得良好的鲁棒/性能平衡．最后,将控制器的参数整定转化为一个约束优化问题,提出控制器解析整定方法,并通过仿真实例验证该方法的有效性．     

时变不确定切换广义系统的鲁棒最优保性能控制

针对一类时变参数不确定切换广义系统,对其鲁棒最优保性能控制问题进行研究,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。通过构造广义Lyapunov函数和线性矩阵不等式方法,给出系统鲁棒最优保性能控制器存在的充分条件。进一步,建立一个具有线性矩阵不等式约束的凸优化问题,得到鲁棒最优保性能控制律及闭环性能指标上界。最后用示例说明该方法的有效性。     

带不确定时滞的中立型系统之鲁棒非脆弱保性能控制

针对一类动态不确定时滞中立型系统,研究了非脆弱鲁棒保性能控制器设计问题.考虑的中立型系统和状态反馈控制器均具有不确定性.在适当的假设下利用Lyapunov稳定性方法,以线性矩阵不等式的形式,给出了使该动态时滞不确定中立型系统二次稳定及非脆弱鲁棒保性能状态反馈控制器存在的充分条件.通过求解相应的线性矩阵不等式就可得到系统的非脆弱鲁棒保性能控制器,同时也能保证二次性能函数不超过一个确定的界.最后,用数值仿真验证了所给方法的可行性.     

永磁同步电动机的鲁棒MR-ILQ 最优电流控制

提出了永磁同步电动机鲁棒参考模型逆线性二次型最优电流控制系统的结构和数学模型，设计了最优电流控制系统的伺服控制器，分析了系统的鲁棒稳定性和鲁棒跟踪性能．以内埋式永磁同步电动机为例，对系统进行了仿真研究．仿真结果表明，系统对参数变化和负载扰动具有很强的鲁棒性，可以实现高精度的电流控制和动态解耦。     

不确定条件下控制分配问题的鲁棒优化方法

针对具有冗余执行机构的过驱动系统, 在考虑控制效率不确定性的条件下, 提出了一种基于鲁棒优化理论的控制分配算法. 研究了原始不确定鲁棒优化模型的建立和基于椭球不确定集的鲁棒对等式的转化问题, 并推广到可由锥二次不等式表示的不确定集的情况. 讨论了鲁棒优化控制分配算法的求解方法及其计算复杂度. 最后, 针对多操纵面飞机的最优控制分配问题与传统算法进行了仿真比较, 结果表明鲁棒优化算法能有效降低控制效率不确定性的影响, 使分配结果更为合理, 从而具有更好的鲁棒性, 同时能有效提高操纵面故障情况下闭环系统的控制重构能力, 很好地改善了飞控系统的性能.     

Robust controller synthesis via shifted parameter-dependentquadratic cost bounds

Parameterized Lyapunov bounds and shifted quadratic guaranteed cost bounds are merged to develop shifted parameter-dependent quadratic cost bounds for robust stability and robust performance. Robust fixed-order (i.e., full- and reduced-order) controllers are developed based on new shifted parameter-dependent bounding functions. A numerical example is presented to demonstrate the effectiveness of the proposed approach     

Robust reliability method for non-fragile guaranteed cost control of parametric uncertain systems

The problem of non-fragile guaranteed cost control of uncertain systems is studied from a new point of view of reliability against uncertainties. An efficient robust reliability method for the analysis and design of non-fragile guaranteed cost controller of parametric uncertain systems is presented systematically. By the method, a robust reliability measure of an uncertain control system satisfying required robust performance can be obtained, and the robustness bounds of uncertain parameters such that the control cost of a system is guaranteed can be provided. The optimal non-fragile guaranteed cost controller obtained in the paper may possess optimal guaranteed cost performance satisfying the precondition that the system is robustly reliable with respect to uncertainties occurring in both the controlled plant and controller gain. The presented formulations are in the framework of linear matrix inequality and thus can be carried out conveniently. The presented method provides an essential basis for the tradeoff between reliability and control cost in controller design of uncertain systems. Two numerical examples are provided to demonstrate the efficiency and feasibility of the presented method. It is shown that the coordination and simultaneous realization of the system performance, control cost, and robust reliability in control design of uncertain systems are significant.     

Polynomial Design of Optimal Sampled-Data Tracking Systems: II. Robust Optimization

A direct method for robust sampled-data tracking systems design is presented. The method is based on the use of Laplace transformation in continuous time and polynomial equation theory. A criterion is proposed for robust optimization of sampled-data tracking systems. The structure of the optimal robust controller transfer function is investigated and its order is determined explicitly. The relations between robust and quadratic optimization problems are established. A mixed optimization problem is considered, when the cost function includes the integral quadratic error and a robustness term.     

基于LMI 的不确定随机系统输出反馈保性能控制

针对一类不确定连续随机系统,研究了具有输出反馈控制器的保性能控制．首先,对于范数有界 的不确定随机系统,得到了具有输出反馈控制器的闭环系统的二次型性能指标的上界一般形式．其次,应用 线性矩阵不等式技术,研究了其闭环系统的二次稳定和二次保性能稳定;并且依据线性矩阵不等式优化方法, 得到了使闭环系统渐近稳定的最优输出反馈保性能控制器．最后,给出仿真算例,验证本文方法的可行性和 有效性．     

不确定奇异时滞系统的保性能控制

利用线性矩阵不等式方法,讨论不确定性奇异时滞系统的保性能控制问题,给出了问题可解的一个充分条件和保性能鲁棒控制器的设计,以及相应的可保性能指标.最后举例说明了所提出方法的正确性.     

不确定时滞系统的保代价H∞鲁棒可靠控制

针对一类不确定时滞受扰系统,研究了在执行器发生故障情况下系统具有保代价的H_∞鲁棒可靠控制器设计问题。根据Lyapunov稳定性理论,得到了系统存在保代价H_∞鲁棒可靠控制器应满足的一个矩阵不等式,进一步将这个矩阵不等式转化为线性矩阵不等式（LMI）,并给出了系统状态反馈控制器的设计方法。利用论文方法设计的鲁棒可靠控制器能够使得时滞系统对于任意允许的不确定量以及一个预先指定执行器子集中任意执行器失效不仅具有鲁棒容错性,并且使系统存在保成本上界以及具有指定H∞范数的干扰抑制能力。仿真结果表明了该可靠控制器设计方法的有效性。     

Robust reliable guaranteed cost control of positive interval systems with multiple time delays and actuator failure

This paper addresses the robust reliable guaranteed cost control problem of positive interval systems with multiple time delays and actuator failure for a given quadratic cost function. Through constructing a Lyapunov–Krasovskii functional, a sufficient condition for the existence of robust reliable guaranteed cost controllers is established such that the closed-loop system is positive and asymptotically stable, and the cost function is guaranteed to be no more than a certain upper bound. Based on the linear matrix inequality method, a criterion for the design of robust reliable guaranteed cost controllers is derived which can tolerate all admissible uncertainties as well as actuator failure. Moreover, a convex optimisation problem with linear matrix inequality constraints is formulated to design the optimal robust reliable guaranteed cost controller which minimises the upper bound of the closed-loop system cost. A numerical example is given to show the effectiveness of the proposed methods.     

On delay‐dependent LMI‐based guaranteed cost control of uncertain neutral systems with discrete and distributed time‐varying delays

In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov–Krasovskii functional theory, a delay‐dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed‐loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd.