Minimax controller design for a class of uncertain linear systems
type: Item
instance of: scholarly article
title: Minimax controller design for a class of uncertain linear systems
zbMATH Open document ID: 0931.93025
DOI: 10.1016/S0005-1098(98)00162-9
author: Paul Milliken
author: Clive Marsh
author: B. Van Brunt
published in: Automatica
publication date: 2000-02-20T00:00:00Z
review text: The paper presents results on the design of minimax controllers for a class of uncertain linear systems. The system is subject to disturbance inputs which are related to the disturbance outputs by a system representing the structured uncertainty. Each uncertainty input is bounded by an integral quadratic constraint. The system performance is measured by an integral quadratic cost function. The results are closely related to that of \textit{A. V. Savkin} and \textit{I. R. Petersen} [IEEE Trans. Autom. Control, AC-39, 1971-1977 (1995; Zbl 0829.49003)]. The present paper gives a new proof of minimax optimality. It is shown that, to design a minimax controller, an objective function dependent upon the solution of a parametric Riccati equation has to be optimized with respect to the parameters. This objective function is shown to be convex over the set of feasible parameters. The application of the proposed method is illustrated by a numerical example.
Mathematics Subject Classification ID: 93B51
Mathematics Subject Classification ID: 49N10
Mathematics Subject Classification ID: 93B35
zbMATH DE Number: 1331861
zbMATH Keywords: minimax techniques
zbMATH Keywords: structured uncertainty
zbMATH Keywords: convex optimization
zbMATH Keywords: state feedback
zbMATH Keywords: integral quadratic constraint
reviewed by: É. Gyurkovics
MaRDI profile type: Publication
full work available at URL: s0005-1098(98)00162-9
OpenAlex ID: W2061894916
Wikidata QID: Q131226543
Recommended article: Control of Uncertain (min,+)-Linear Systems
Recommended article: Min-max control of constrained uncertain discrete-time linear systems
Recommended article: Minimax optimal control of linear system with input-dependent uncertainty
Recommended article: Min-max optimal control of linear systems with uncertainty and terminal state constraints
Recommended article: Minimax optimal control for one class of uncertain systems
Recommended article: Minimax control for a class of linear systems subject to disturbances
Recommended article: Q4879518
Recommended article: Minimax optimal control of uncertain systems with structured uncertainty
Recommended article: Design of optimal control under uncertain initial conditions: a minimax approach
Recommended article: Q3496271
description: scientific article; zbMATH DE number 1331861