Impulsive and impulse-free PD solutions of singular LQ control

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2025-02-01 DOI:10.1016/j.sysconle.2025.106024

Jovan Stefanovski

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引用次数: 0

Abstract

This paper addresses the singular linear–quadratic (LQ) control problem, considering cases with or without impulses in the state, and with or without stability. The optimal controller obtained includes a derivative of the state. The assumptions made are system stabilizability and the left-invertibility of the plant transfer matrix. Necessary and sufficient conditions for stability and the impulse-freeness of the optimal state are provided. These conditions are related to the absence of invariant zeros on the imaginary axis, and at infinity with orders greater than one, as well as to strong

^{*}

detectability. When these conditions are not met, the subspace ensuring that the optimal state is impulse-free, if the initial state belongs to that subspace, is determined. Additionally, a suboptimal yet practically realizable controller is presented, along with an explicit expression for the difference between the cost functional values corresponding to the suboptimal and optimal controllers. Illustrative examples are included.

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奇异 LQ 控制的脉冲和无脉冲 PD 解

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来源期刊

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.