Delta算子系统具有极点约束的鲁棒非脆弱方差控制

研究Delta算子描述的线性不确定系统具有圆形区域极点约束的鲁棒非脆弱方差控制问题. 针对系统参数范数有界不确定性和控制器的乘性增益不确定性, 运用线性矩阵不等式(LMI)方法, 提出具有圆形区域极点约束的状态反馈鲁棒非脆弱方差控制器存在的条件和设计方法. 数值算例表明设计方法的可行性.     

方差约束下线性连续系统的多指标随机控制

本文由部分组成，第一部分考虑具有给定Ｈ∞范数，圆形区域极点及稳态方差约束的线性连续系统的控制器设计问题，第二部分则进一步研究方差及圆形区域极点的约束下不确定性连续系统的性能鲁棒控制器设计问题，文中提出有效的代数黎卡提方程方法来解决如上问题，并用数值算例说明所提方法的直接与可行性。     

连续系统的约束方差／H_∞综合设计

考虑线性连续随机系统在稳态方差及Ｈ∞指标约束下的综合设计问题，即寻找状态反馈控制器，使闭环系统每个状态分量的稳态方差满足各自预先给定的约束，同时从噪声输入到系统输出的传递函数的Ｈ∞范数也满足预先给定的约束。本文绘出了期望控制器的存在条件及解析表达式，并用算例说明文中设计方法的直接性与有效性。     

连续系统的约束方差／H∝综合设计

考虑线性连续随机系统在稳态方差及Ｈ∝指标约束下的综合设计问题，即寻找状态反馈控制器，使闭环系统每个状态分量的稳态方差满足各自预先给定的约束，同时从噪声输入到系统输出的传递函数的Ｈ∝范数也满足预先给定的约束。本文给出了期望控制器的存在条件及解析表达式，并用算例说明文中设计方法的直接性与有效性。     

误差方差及圆形区域极点约束下状态估计问题的研究:连续时间情形

提出并讨论了线性连续随机系统在稳态估计误差方差及圆形区域极点约束下的状态估 计问题,即希望设计滤波增益,使得每个状态分量的估计误差方差稳态值不大于各自预先给 定值,同时滤波矩阵的极点位于给定圆形区域内,从而使滤波过程具有良好的稳、暂态特性. 文中利用一修正的代数Riccati方程,给出了期望滤波增益的存在条件及解析表达式.数值 例子说明了文中设计方法的直接性和有效性.     

方差约束了不确定线性离散时间系统的鲁棒H_∞控制(英文)

本文考虑具有H∞范数及方差约束的不确定线性离散时间系统的鲁棒控制器设计问题，即设计鲁律控制器，使闭环系统对所有可允的参数扰动保持渐近稳定，同时传递函数满足预先给定的H∞范数约束，且各状态的稳态方差值不大干预先给定值．结果表明，一种有效的代数方法可用来使不确定线性随机离散时间系统满足给定的H∞范数约束及方差约束．     

极点与状态方差约束下的动态输出反馈可靠控制

研究了线性不确定系统区域极点与状态方差约束下的动态输出反馈可靠控制器的设计问题．首先在连续型执行器故障模型下，利用线性矩阵不等式方法，建立了容错控制中区域极点指标与方差上界指标间的相容性理论；然后，应用极值原理分析了与区域极点指标相容的方差上界指标的取值范围；最后，给出了同时满足区域极点与状态方差约束下的动态输出反馈可靠控制器的设计步骤．仿真实例验证了结果的有效性．     

状态反馈中圆形极点与状态方差约束的相容性

对一类线性随机系统的状态反馈问题,研究了两类约束指标:状态方差与圆形区域 极点的相容性,并对具有指定圆形极点及相容状态方差约束的控制问题给出了满意控制设计 方法.用线性矩阵不等式(LMIs)刻划了圆形极点约束下系统存在反馈控制律的充要条件;通 过求解LMIs约束下矩阵迹的极值问题,给出了方差约束指标的较好容许范围;算例说明本 成果简洁、有效.     

离散随机系统的容错约束方差控制设计

本文考虑线性离散随机系统的容错约束方差控制设计问题，即设计反馈控制器，使闭环系统在可能的传感器失效不仅保持渐近稳定，而且满足预先给定的稳态方差约束，文中导出期望了容约束方差控制器存在的充分条件，并进一步给出了其参数化代数表达式。     

区域极点约束下线性离散系统的Riccati鲁棒控制

讨论区域极点约束下,含结构参数扰动的不确定线性离散系统的鲁棒控制问题,即设计一 鲁棒状态反馈控制器,使线性离散系统在可允许的参数扰动下,闭环矩阵极点始终位于一预先 给定的圆形区域中,从而闭环系统具有期望的动态性能.上述控制目的可通过求解一含参数 的代数离散Riccati方程达到.     

Controller design for continuous systems with variance and circular pole constraints

The problem of controller design with variance and circular pole constraints is considered in this paper. The motivation for this problem is twofold: (1) many engineering systems have performance requirements naturally stated in terms of upper bounds on the variances of the system states; and (2) the fine transient properties of the closed-loop system are required in practice. The goal of this problem is to design the controller such that the closed-loop system meets the prespecified variance constraints and circular pole constraints simultaneously. It is shown that a desired controller is determined by using the solution of a modified Lyapunov equation. Necessary and sufficient conditions are given for the existence of desired controllers. The set of desired controllers (if they exist) is also characterized.     

Delta算子系统具有圆形区域极点约束的非脆弱H∞滤波器设计: 一种LMI优化方法

研究了一类Delta算子线性系统具有圆形区域极点配置的非脆弱 H∞滤波器设计问题. 本文的目的是设计滤波器使得滤波误差系统不仅满足给定的圆点极点约束或D稳定约束, 而且从扰动输入到滤波误差的传递函数满足给定的 H∞范数约束. 所设计的滤波器具有乘性的滤波器增益变化, 基于Lyapunov稳定性理论和线性矩阵不等式方法, 给出具有区域极点配置的Delta算子离散系统非脆弱 H∞滤波器存在的充分条件. 数值仿真例子说明设计方法的有效性以及所提设计方法具有更小的保守性.     

基于极点与输出方差约束相容性分析的状态反馈

研究一类线性随机系统的满意状态反馈,期望闭环系统同时满足给定的圆形极点与输出方差约束,先分析这两类约束指标的相容性,利用线性矩阵不等式（LMI）方法,给出与极点指标相容的输出方差上界（或下界）指标的较好取值范围,然后,对具有相容极点与输出方差指标的控制问题,给出设计理论,特别对输出方差指标是区间的情形提出一种控制设计方法,算例对所得结果及所提设计方法作了说明。     

Robust state estimation for perturbed systems with error variance and circular pole constraints: The discrete-time case

This paper is concerned with the problem of robust state estimation for linear perturbed discrete-time systems with error variance and circular pole constraints. The goal of this problem addressed is the design of a linear state estimator such that, for all admissible uncertainties in both state and output equations, the following two performance requirements are simultaneously satisfied: (1) the poles of the filtering matrix are all constrained to lie inside a prespecified circular region; and (2) the steady-state variance of the estimation error for each state is not more than the individual prespecified value. It is shown that this problem can be converted to an auxiliary matrix assignment problem and solved by using an algebraic matrix equation/inequality approach. Specifically, the conditions for the existence of desired estimators are obtained and the explicit expression of these estimators is also derived. The main results are then extended to the case when an H performance requirement is added. Finally, a numerical example is presented to demonstrate the significance of the proposed technique.     

Controller design with regional pole constraints

A design procedure is developed that combines linear-quadratic optimal control with regional pole placement. Specifically, a static and dynamic output-feedback control problem is addressed in which the poles of the closed-loop system are constrained to lie in specified regions of the complex plane. These regional pole constraints are embedded within the optimization process by replacing the covariance Lyapunov equation by a modified Lyapunov equation whose solution, in certain cases, leads to an upper bound on the quadratic cost functional. The results include necessary and sufficient conditions for characterizing static output-feedback controllers with bounded performance and regional pole constraints. Sufficient conditions are also presented for the fixed-order (i.e. full- and reduced-order) dynamic output-feedback problem with regional pole constraints. Circular, elliptical, vertical strip, parabolic, and section regions are considered     

具有执行器故障的Delta算子系统D稳定H_∞鲁棒容错控制

研究Delta算子描述的不确定线性系统在区域极点约束和H∞范数界约束下的鲁棒容错控制问题。利用线性矩阵不等式（LMI）理论,给出了在执行器失效情况下Delta算子不确定系统在区域极点约束下的鲁棒H∞容错控制存在的充分条件,并可通过求解LMI得到鲁棒容错控制器的设计。所得结果可将连续系统和离散系统的有关结果统一到Delta算子框架中。数值算例验证了该方法的可行性。     

具有传感器故障的可靠圆盘极点配置

针对线性定常系统，提出了考虑传感器故障的指定圆盘极点配置可靠控制问题，在考虑更一般、更实际的传感器故障模型的基础上，给出了系统将极点配置到指定圆盘内的充分条件，通过求解LMI完成状态反馈控制器的设计，仿真例子验证了该结果的可行性，并进一步说明了对系统进行可靠设计的必要性。     

Robust H∞ control for uncertain discrete-time systems with circular pole constraints

This paper investigates the problem of robust H_∞ control for uncertain discrete-time systems with circular pole constraints. The system under consideration is subject to norm-bounded time-invariant uncertainties in both the state and input matrices. The problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region, and the H_∞ norm of the closed-loop transfer function is strictly less than a given positive scalar for all admissible uncertainties. By introducing the notion of quadratic d stabilizability with an H_∞ norm-bound, the problem is solved. Necessary and sufficient conditions for quadratic d stabilizability with an H_∞ norm-bound are derived. Our results can be regarded as extensions of existing results on robust H_∞ control and robust pole assignment of uncertain systems.