Numerical solution of minimax optimal control problems by multiple shooting technique
type: Item
instance of: scholarly article
title: Numerical solution of minimax optimal control problems by multiple shooting technique
zbMATH Open document ID: 0577.49022
DOI: 10.1007/BF00939277
author: Hans Joachim Oberle
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: This paper presents the application of the multiple shooting technique to minimax optimal control problems (optimal control problems with Chebyshev performance index). A standard transformation is used to convert the minimax problem into an equivalent optimal control problem with state variable inequality constraints. Using this technique, the highly developed theory on the necessary conditions for state-restricted optimal control problems can be applied advantageously. It is shown that, in general, these necessary conditions lead to a boundary-value problem with switching conditions, which can be treated numerically by a special version of the multiple shooting algorithm. The method is tested on the problem of the optimal heating and cooling of a house. This application shows some typical difficulties arising with minimax optimal control problems, i.e., the estimation of the switching structure which is dependent on the parameters of the problem. This difficulty can be overcome by a careful application of a continuity method. Numerical solutions for the example are presented which demonstrate the efficiency of the method proposed.
Mathematics Subject Classification ID: 49M25
Mathematics Subject Classification ID: 49K35
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93B40
zbMATH DE Number: 3923538
zbMATH Keywords: multiple shooting
zbMATH Keywords: minimax optimal control problems
zbMATH Keywords: boundary-value problem with switching conditions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00939277
OpenAlex ID: W1993588807
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description: scientific article; zbMATH DE number 3923538