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

• 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
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04650386/
• 关键词: Systems Characterized by Parameters; Control Systems; Systems Theory; 環上のシステム; 非干渉制御; パラメータを含む線形システム; 環上の線形システム

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

本研究涉及一族S的动力系统S（lambda），其特征在于q（（）SY ≥.（）0）真实的参数lambda = [λ da_1，λ da_2，···，lambda_q]，形式为其中X是状态空间，LAMBDA * R^q是给定集合。本文的目的是用数学和系统理论的术语来描述这样一个族，研究这个族的各种数学结构，并将这些结果应用于重要的控制问题。为了简化研究，假设每个系统S（lambda）是线性的，并且以多项式形式依赖于参数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，对于情况（a）和（B）得到的主要结果总结如下. (a)当q = 1时，族S可以被描述为定义在主理想域上的单个线性系统，并且干扰解耦问题和块三角解耦问题是 ...更多信息 研究得到一些可解性条件。对于q（）SY ≥（）2，族S可以表示为唯一分解域上的单个线性系统，并研究了各种控制问题。特别地，得到了块解耦问题可解的充分必要条件。最后，给出了一个有限线性系统集，考虑了由这些系统的凸组合所刻画的系统的各种解耦问题，并证明了它们可解的一些充要条件。(b)对于给定的两个无穷维系统，将一个系统表示为两个系统的凸组合，作为q = 1的特殊情况。最后，利用一个符号操作系统MAPLE，构造了各种计算机系统，对所得结果进行了实际应用所需的符号和数值计算。少

项目成果

王維本,稲葉博: "一意分解整域上の線形システムのブロック非干渉化について" システム制御情報学会論文誌. 6. 171-179 (1993)

Weiben Wang、Hiroshi Inaba：“关于独特分解域上线性系统的块解耦”系统、控制和信息工程师学会汇刊 6. 171-179 (1993)。

W.wang and H.Inaba: "Decouplability of Injective Multivariable Linear Systems" Transactions of The Society of Instrument and Control Engineers. Vol.28, No.5. 564-569 (1992)

W.wang 和 H.Inaba：“单射多变量线性系统的解耦性”仪器与控制工程师学会会刊。

W.wang and H.Inaba: "Block Decoupling for Linear Systems over Unique Factorization Domains" Transactions of The Institute of Systems, Control and Information Engineers. Vol.6, No.4. 171-179 (1993)

W.wang 和 H.Inaba：“独特因式分解域上的线性系统的块解耦”系统、控制和信息工程师学会汇刊。

王 維本,: "一意分解整域上の線形システムのブロック非干渉化について" システム制御情報学会論文誌. 6. 171-179 (1993)

Weiben Wang，：“关于独特分解域上线性系统的块解耦”，系统、控制和信息工程师学会汇刊，6. 171-179 (1993)。

王維本,稲葉博: "単射的多変数形システムの非干渉化可能条件" 計測自動制御学会論文集. 28. 564-569 (1992)

Weiben Wang、Hiroshi Inaba：“实现单射多变量系统解耦的条件”仪器与控制工程师协会会议记录 28. 564-569 (1992)。