Application of the averaging method for construction of suboptimal solutions to singularly perturbed optimal control problems
type: Item
instance of: scholarly article
title: Application of the averaging method for construction of suboptimal solutions to singularly perturbed optimal control problems
zbMATH Open document ID: 0592.49023
published in: Automation and Remote Control
publication date: 1985-01-01T00:00:00Z
review text: The paper deals with a nonlinear singularly perturbed system. Using the idea of the averaging method, applied to the presentation of this system in the ''expanded'' time scale, the author introduces a differential inclusion whose trajectories approximate the ''slow'' parts of the trajectories of the original system. Estimations of the accuracy of this approximation are given without proofs. The approach is applied to optimal control problems for a system which is linear and asymptotically stable with respect to the ''fast'' variable.
Mathematics Subject Classification ID: 49M27
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 3951412
zbMATH Keywords: nonlinear singularly perturbed system
zbMATH Keywords: averaging
zbMATH Keywords: differential inclusion
zbMATH Keywords: approximation
author: V. Gaitsgory
reviewed by: Vladimir M. Veliov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3951412