Constrained LQR problems governed by the potential equation on Lipschitz domains with point observations
type: Item
instance of: scholarly article
title: Constrained LQR problems governed by the potential equation on Lipschitz domains with point observations
zbMATH Open document ID: 0846.49018
author: Zhonghai Ding
author: Jianxin Zhou
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1996-09-12T00:00:00Z
review text: Using layer potential theory and boundary element methods, the authors study linear quadratic regulator problems governed by the potential equation on Lipschitz domains, with point observations on the boundary. First, the linear quadratic regular problems without control constraints are studied. It is proved that in \(\mathbb{R}^3\), the linear quadratic regulator problem generally does not have any nontrivial optimal control, whereas in \(\mathbb{R}^2\), it has a unique optimal control. The explicit characterization and regularity of the optimal control are derived. Then the linear quadratic regulator problems with control constraints are discussed. In both \(\mathbb{R}^2\) and \(\mathbb{R}^3\), it is obtained the existence, uniqueness, regularity and an explicit characterization of the optimal control. Finally a decomposition of the optimal control of linear quadratic regulator problems on polygonal domains is established, which is very useful in the regularity analysis and numerical computation. Based upon the decomposition formula, a numerical algorithm insensitive of the boundary discretization is developed. Several numerical examples are included to illustrate the results.
Mathematics Subject Classification ID: 49N10
Mathematics Subject Classification ID: 31A10
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 93C20
zbMATH DE Number: 891044
zbMATH Keywords: linear quadratic regulator
zbMATH Keywords: layer potential theory
zbMATH Keywords: Lipschitz domain
zbMATH Keywords: boundary control
zbMATH Keywords: point observation
zbMATH Keywords: boundary element method
zbMATH Keywords: numerical algorithm
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 891044