Control of singularly perturbed hybrid stochastic systems

J. A. Filar*, V. Gaitsgory, A. Haurie

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

3 Citations (Scopus)

Abstract

In this paper we study a class of optimal stochastic control problems involving two different time scales. The fast mode of the system is represented by deterministic state equations whereas the slow mode of the system corresponds to a jump disturbance process. Under a fundamental ''ergodicity'' property for a class of ''infinitesimal control systems'' associated with the fast mode, we show that there exists a limit problem which provides a good approximation to the optimal control of the perturbed system. Both the finite and infinite discounted horizon cases are considered. We show how an approximate optimal control law can be constructed from the solution of the limit control problem. In the particular case where the infinitesimal control systems possess the so-called turnpike property, i.e. are characterized by the existence of global attrators, the limit control problem can be given an interpretation related to a decomposition approach. Due to the constraints on page numbers all results are presented without proofs. Full details will be supplied in a follow up paper by the same authors.

Original languageEnglish
Title of host publicationProceedings of the 35th ieee conference on decision and control
Place of PublicationPiscataway, NJ
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages511-516
Number of pages6
Volume1
ISBN (Print)0780335902
DOIs
Publication statusPublished - 1996
Externally publishedYes
Event35th IEEE Conference on Decision and Control - KOBE, Japan
Duration: 11 Dec 199613 Dec 1996

Publication series

NameIEEE CONFERENCE ON DECISION AND CONTROL - PROCEEDINGS
PublisherI E E E
ISSN (Print)0191-2216

Conference

Conference35th IEEE Conference on Decision and Control
CountryJapan
CityKOBE
Period11/12/9613/12/96

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