Integral manifolds and decomposition of singularly perturbed systems
type: Item
instance of: scholarly article
title: Integral manifolds and decomposition of singularly perturbed systems
zbMATH Open document ID: 0552.93017
DOI: 10.1016/S0167-6911(84)80099-7
published in: Systems \& Control Letters
publication date: 1984-01-01T00:00:00Z
review text: The paper uses the method of integral manifolds to find a transformation under which the singularly perturbed system of differential equations \[ \dot x=f(t,x,y,\epsilon),\quad \epsilon \dot y=g(t,x,y,\epsilon) \] reduces to \[ \dot u=F(t,u,\epsilon),\quad \epsilon \dot v=G(t,u,v,\epsilon). \] The assumptions are similar to those in Tichonov's theorem, i.e. the eigenvalues of the matrix \((\partial g/\delta y)\{t,x,h_ 0(t,x),0)\), where \(h_ 0(t,x)\) is the isolated solution of \(g(t,x,y,0)=0\), have strictly negative real parts. A transformation with the above properties is given for linear systems. As an application, the linear boundary value problem that arises in linear- quadratic optimal control is considered. The transformation helps to obtain an asymptotic expansion of the solution.
Mathematics Subject Classification ID: 93B17
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 3880520
zbMATH Keywords: integral manifolds
zbMATH Keywords: singularly perturbed system
zbMATH Keywords: linear-quadratic optimal control
author: V. A. Sobolev
reviewed by: A. L. Dontchev
MaRDI profile type: Publication
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full work available at URL: s0167-6911(84)80099-7
OpenAlex ID: W1985115913
description: scientific article; zbMATH DE number 3880520