Limit occupational measures set for a control system and averaging of singularity perturbed control systems
type: Item
instance of: scholarly article
title: Limit occupational measures set for a control system and averaging of singularity perturbed control systems
zbMATH Open document ID: 0927.93007
author: Arie Leizarowitz
author: V. Gaitsgory
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-12-13T00:00:00Z
review text: This paper investigates the asymptotic behaviour of the so-called occupational probability \[ {1\over s}\lambda \biggl\{ \tau\in [0,S]/ \bigl(y(\tau), u(\tau)\bigr) \in Q\biggr\} \] where \(Q\) is a given set and \((y, u)\) are associated with a control system \[ y'(\tau)= g\bigl(y (\tau),u(\tau) \bigr) \quad \tau\in [0,S]. \] The existence of a limit of such an occupational measure when \(s\to+\infty\) is given. For a singular perturbation control problem, the authors prove that the slow variables can be approached by solutions to a differential inclusion obtained through the limit of suitable occupational measures.
reviewed by: Marc Quincampoix
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 93C70
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 1295256
zbMATH Keywords: approximation
zbMATH Keywords: singular perturbation
zbMATH Keywords: differential inclusion
zbMATH Keywords: occupational measures
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6281
OpenAlex ID: W2088348409
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DOI: 10.1006/JMAA.1999.6281
description: scientific article; zbMATH DE number 1295256