Controller design to optimize a composite performance measure
type: Item
instance of: scholarly article
title: Controller design to optimize a composite performance measure
zbMATH Open document ID: 0878.93024
DOI: 10.1007/BF02192284
author: O. Diekmann
published in: Journal of Optimization Theory and Applications
publication date: 1997-07-06T00:00:00Z
review text: This paper studies a mixed objective problem of minimizing a composite measure of the \(l_1\)-norm, the \(H_2\)-norm, and the \(l_\infty\)-norms of the step and pulse responses respectively of the closed loop over all stabilizing controllers. Employing a variant of the Kuhn-Tucker-Lagrange duality theorem, it is shown that the problem is equivalent to a finite-dimensional convex optimization problem with an a priori known dimension. The solution is unique and represents a Pareto-optimal point with respect to the individual measures involved. It is also shown that the optimal solution is continuous with respect to changes in the coefficients of the composite measure. The problem is analyzed for discrete-time, single-input single-output, linear time-invariant systems.
Mathematics Subject Classification ID: 93B50
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 1031434
zbMATH Keywords: \(l_ 1\)-optimization
zbMATH Keywords: multiobjective control
zbMATH Keywords: Kuhn-Tucker-Lagrange duality
zbMATH Keywords: convex optimization
zbMATH Keywords: Pareto-optimal point
reviewed by: Toshihiro Kobayashi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1031434