\(H_ \infty\) optimal control for symmetric linear systems
type: Item
instance of: scholarly article
title: \(H_ \infty\) optimal control for symmetric linear systems
zbMATH Open document ID: 0826.49001
DOI: 10.1007/BF03167205
author: Satoru Iwata
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1995-11-16T00:00:00Z
review text: Let \(G(s)\) be a real-rational proper transfer matrix of a time-invariant linear system. Denote by \(Q\) and \(R\) orthogonal representations of a finite group \(A\) given on the input space \(U\) and output space \(Y\), respectively. \(G(s)\) is called symmetric (or invariant) with respect to \(A\) if \(R(g) G(s)= G(s) Q(g)\), for any \(g\) from \(A\). The standard \(H_\infty\)-control problem is called \(A\)-symmetric with respect to \(A\) (or invariant) if the plant transfer matrix \(P\) is \(A\)-symmetric. The model matching problem is called symmetric if its three transfer matrices are symmetric. Providing, first, that a symmetric standard problem can be reduced to a symmetric model matching problem, and, second, that the latter has a symmetric \(H_\infty\)-optimal solution, it is shown that the symmetric standard problem has a symmetric optimal solution. Two numerical computation approaches are proposed to solve an \(A\)- symmetric \(H_\infty\)-standard control problem. The first one uses the \(A\)-symmetry of the two Riccati equations to get an \(A\)-symmetric central solution, while the second one uses block-diagonalization of \(A\)- symmetric matrices and decomposition of the problem into subproblems of lower dimensions.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93B36
zbMATH DE Number: 446763
zbMATH Keywords: \(H_ \infty\)-optimal control
zbMATH Keywords: symmetric linear systems
zbMATH Keywords: symmetric optimal solution
zbMATH Keywords: Riccati equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 446763