Direct scheme in optimal control problems with fast and slow motions
type: Item
instance of: scholarly article
title: Direct scheme in optimal control problems with fast and slow motions
zbMATH Open document ID: 0609.49022
DOI: 10.1016/0167-6911(86)90071-X
author: S. V. Belokopytov
author: Mikhail Dmitriev
published in: Systems \& Control Letters
publication date: 1986-01-01T00:00:00Z
review text: The authors consider the problem \[ \min \{G(x(T),y(T))+\int^{T}_{0}F(x,y,u,t)dt\} \] subject to \[ \dot x=f(x,y,u,t),\quad \epsilon \dot y=g(x,y,u,t) \] where \(\epsilon\) is a small parameter. The unknown functions x, y and u are sought as asymptotic series, according to the method of the boundary layer functions. It is shown, that each order term can be found by solving three lower dimensional optimal control problems, corresponding to the regular and to the boundary layer components. Results concerning the convergence of the above scheme are also presented.
Mathematics Subject Classification ID: 49M27
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 93B40
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 3986042
zbMATH Keywords: control problems with fast and slow motions
zbMATH Keywords: asymptotic series
zbMATH Keywords: boundary layer functions
zbMATH Keywords: convergence
reviewed by: Vladimir M. Veliov
MaRDI profile type: Publication
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full work available at URL: 0167-6911(86)90071-x
OpenAlex ID: W2086872762
description: scientific article; zbMATH DE number 3986042