A Theory of Systems Characterized by Parameters and It's Application to Control Systems

参数表征系统理论及其在控制系统中的应用

基本信息

批准号：
04650386
负责人：
INABA Hiroshi
金额：
$ 1.22万
依托单位：
Tokyo Denki University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1992
资助国家：
日本
起止时间：
1992 至 1993
项目状态：
已结题

项目摘要

This study is concerned with a family S of dynamical systems S(lambda) characterized by q((〕SY.gtoreq.〔) 0) real parameters lambda = [lambda_1, lambda_2, ・・・, lambda_q] in the form where X is the state space and LAMBDA * R^q is a given set. The purpose of this stydy is to describe such a family in mathematical and system theoretical terminologies, to investigate various mathematical structures of the family and to apply these results to important control problems. To simplify the development, it is assumed that each system S(lambda) is linear and depends on the parameters lambda in polynomial form, and the family S is investigated in the following two cases : (a) X is finite dimensional and (b) X is infinite dimensional.The main results obtained for cases (a) and (b) are summarized as follows.(a) For q = 1, the family S can be described as a single linear system defined over a principal ideal domain, and the disturbance decoupling problem and the block triangular decoupling problem are … More studied to obtain some solvability conditions. For q (〕SY.gtoreq.〔) 2, the family S can be represented as a single linear system over a unique factorization domain, and various control problems are examined. In particular, necessary and sufficient conditions for the block decoupling problem to be solvable are obtained. Finally, given a finite set of linear systems, various decoupling problems are considered for a system characterized as a convex combination of these systems, and some necessary and/or sufficient conditions for their solvability are proved.(b) For given two infinite dimensional systems, a system which is represented as convex combination of the two system is considered as a special case of q = 1. Some sufficient conditions for this system to be rejected from disturbance are obtained.Finally, using a symbolic manipulation system MAPLE, various computer systems are constructed to perform symbolic and numerical computations necessary for practical applications of the obtained results. Less

本研究涉及动力系统 S(lambda) 的族 S，其特征为 q((〕SY.gtoreq.〔) 0) 实参数 lambda = [lambda_1, lambda_2, ..., lambda_q]，其形式为其中 X 为状态空间和 LAMBDA * R^q 是一个给定的集合本研究的目的是用数学和系统理论术语来描述这样一个族，以研究的各种数学结构。为了简化开发，假设每个系统 S(lambda) 是线性的并且取决于多项式形式的参数 lambda，并且在以下两种情况下研究了族 S。：（a）X是有限维的，（b）X是无限维的。情况（a）和（b）获得的主要结果总结如下。（a）对于q = 1，族S可以描述为定义在一个单一的线性系统主理想域，并研究了扰动解耦问题和分块三角解耦问题，得到了一些可解性条件。对于q(〕SY.gtoreq.〔)2，族S可以表示为a上的单个线性系统。独特的因式分解域，以及各种控制问题，特别是，获得了块解耦问题可解的必要和充分条件。对于表征为这些系统的凸组合的系统，考虑解耦问题，并证明了其可解性的一些必要和/或充分条件。(b) 对于给定的两个无限维系统，将系统表示为凸组合的系统两个系统被认为是 q = 1 的特殊情况。获得了该系统免受扰动的一些充分条件。最后，使用符号处理系统 MAPLE，构建了各种计算机系统来执行以下必要的符号和数值计算：所得结果的实际应用较少。