指定圆形极点配置区域输出无偏的输出反馈协方差控制器设计

系统输出无偏性及稳态状态协方差是随机系统的两个重要稳态性能指标，系统的动态品质主要决定于系统的闭环极点位置。本文给出的输出反馈协方差控制器能确保系统：１）闭环极点位于指定圆形配置区域；２）稳态协方差满足既定的上限约束；３）稳态输出无偏。     

关于离散系统的有限拍协方差控制器

在随机控制问题中，性能指林常常表示为系统状态协方差的形式．本文将讨论如下问题．即设计线性反馈控制器，使系统的状态协方差在有限拍内达到其稳态值，同时该稳态值达到预先指定值．本文讨论了这类反馈控制器的存在条件及设计方法，并给出了直接的设计步骤．     

多变量系统传递函数阵极点的结构化配置问题

本文讨论多变量系统传递函数阵极点的结构化配置问题，并基于一类可控规范形给出实现极点结构化配置的状态反馈阵的算法，证明了算法存在的充要条件。     

基于区域极点配置的状态观测器的统一代数刻划

研究了线性定常系统状态观测器区域极点的配置问题，给出了极点配置于圆形区域内的所有状态观测器的代数集合表达式，为状态观测器在工程实际中，如故障检测等应用中满足多性能指标的约束提供了理论指导。     

稳定反馈空间的拓扑结构

本文讨论控制系统反馈空间的拓扑结构.首先讨论线性情况.然后,将其结果推广到非 线性的情况.赋予线性反馈集合以Rn×m拓扑(其中n为状态空间维数,m为输入维数),在这 个拓扑下研究完全能控系统稳定反馈集合的几何结构.文中证明了稳定反馈集合的拓扑结构 与具体系统无关.并且,对较小维数的系统(n≤5)给出了具体的拓扑结构.     

二维线性系统特征结构配置的两种新算法

本文提出了二维线性系统特征结构配置的两种新算法,并给出了状态反馈矩阵存在的充分条件。     

广义状态系统的反馈和极点配置

本文讨论线性反馈对连续时间广义状态空间结构的影响和消去脉冲运动的充分必要条件。给出一个利用输出反馈配置极点的方法。     

干扰解耦和极点配置组合问题的研究*

本文用代数方法研究了干扰解耦和极点配置组合问题,导得了存在一个状态反馈控制器使得干扰—输出完全解耦且同时配置闭环系统全部(或部分)极点的充分条件,给出了实现干扰解耦和极点配置的状态反馈阵的一个检验算法。     

关于状态反馈预测控制系统的极点配置

讨论按极点配置方法的设计问题,给出极点可任意配置的充分必要条件。基于状态空间模型,给出按极点配置方法设计时选取预测时域的方法。通过引入控制作用衰减系数及状态反馈加权系数,状态反馈预测控制系统的极点可任意配置。设计参数实时在线调整方便,增强了预测模型的适应范围,使预测控制系统具有较好的的控制性能和鲁棒性。     

闭环系统的极点配置

本文利用文献[1,2]给出的完全能控系统的控制结构相伴标准形的特点,以及它与多项 式矩阵的直接联系,给出了在状态反馈下,任意配置闭环系统极点的两种方法.状态反馈阵K 是容易确定的.进一步,还给出了具有已给定结构形式的,并有指定的不变因子的多项式方阵 的配置算法.上述这些方法,都便于在计算机上实现.     

Synthesis of Covariance Controllers on the Basis of the System Embedding Technology

A new approach to the synthesis of stochastic control systems, which is called the theory of covariance control, is set out in this paper. Its essence involves securing a prescribed steady-state value of the state covariance matrix of a linear system with the aid of feedback. The necessary and sufficient conditions of the attainability of the state covariance matrix are defined and formulas for the entire set of stabilizing covariance controllers are derived.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 126–137.Original Russian Text Copyright © 2005 by Sel’vesyuk.     

An improved covariance assignment theory for discrete systems

For discrete systems, the set of all state covariances X which can be assigned to the closed-loop system via a dynamic controller is characterized explicitly. For any assignable state covariance X , the set of all controllers that assign this X to the closed-loop system is parameterized with an arbitrary orthonormal matrix U of proper dimension     

All covariance controllers for linear discrete-time systems

The authors characterize the set of covariances that a linear discrete-time plant with a specified-order controller can have. The controllers that assign such covariances to any linear discrete-time system are given explicitly in closed form. The freedom in these covariance controllers is explicit and is parameterized by two orthogonal matrices. By appropriately choosing these free parameters, additional system objectives can be achieved without altering the state covariance, and the stability of the closed-loop system is guaranteed     

Upper bound covariance control of discrete perturbed systems

The purpose of this paper is to develop a methodology, which is based on the state covariance assignment theory, to design feedback controllers such that a specified state covariance upper bound will be achieved. Furthermore, an example is given to illustrate the effectiveness of the present approach.     

A theory of state covariance assignment for discrete systems

In many regulation control problems it is desired to design the controller so that various system states have acceptable root mean squared values. This is a multiple objective problem. One way to satisfy these objectives is to assign a specified state covariance to the system. This paper introduces and solves the following problem: 1) characterize the entire set of state covariances which may be assigned to a linear discrete-time system by state feedback; and 2) find the set of all state feedback gains which will assign an admissible state covariance to the system. Extensions are also presented for state estimate feedback.     

Minimal energy covariance control

In general, the covariance controller which assigns a specified state covariance X to the system is not unique, and the whole set of such controllers can be parametrized by a skew-symmetric matrix S of appropriate dimension. This paper describes how to minimize the control energy by using this freedom and reveals some properties of closed-loop system poles with respect to S.     

Optimal linear stochastic systems with independent controllers

The problem of synthesis of optimal controllers for linear stochastic systems with independent control channels is considered. In the considered systems two independent controllers with independent measurement devices are used. The equations for optimal cost function, covariance matrix of the state estimation error and for the controlled system output are derived. It is shown that the application of a well-known separation principle or certainty equivalence principle results in controllers which are not optimal and which can be far from the optimality. It is also shown that improvement of the estimation accuracy by means of manipulation of the controller parameters can significantly improve the control performance as a whole. The numerical examples of calculation of the optimal independent controllers are given to demonstrate the obtained theoretical results and superiorities over controllers based on the separation principle. It is also demonstrated that the optimal controllers have smaller control gains for the control loops with larger observation noises, which can be characterized as cautious properties of the controllers.     

离散非线性系统的鲁棒模糊协方差控制

针对T-S模糊模型描述的一类不确定非线性离散系统，研究使闭环系统的稳态方差小于某个给定上界，同时闭环极点位于给定圆盘中的状态反馈鲁棒协方差控制律设计问题，并导出以一组线性矩阵不等式表示的控制律的存在条件。     

An optimal controller reduction by covariance equivalent realizations

Based upon the theory of covariance equivalent realizations [1], this note presents a technique to obtain reduced-order controllers via an optimal projection of full-order LQG-controllers. This projection is optimal in the sense that it is a weighted least square approximation to a covariance equivalent projection of the full-order optimal closed-loop system. The technique, which is capable of extracting optimal, minimal LQG-controllers whenever they exist, is also shown to yield controllers that are equivalent to those obtained by component cost analysis [12].     

Upper and lower covariance bounds for perturbed linear systems

Both upper and lower bounds are established for state covariance matrices under parameter perturbations of the plant. The motivation for this study lies in the fact that many robustness properties of linear systems are given explicitly in terms of the state covariance matrix. Moreover, there exists a theory for control by covariance assignment. The results provide robustness properties of these covariance controllers