Control of singularly perturbed hybrid stochastic systems

Jerzy A. Filar*, Vladimir Gaitsgory, Alain B. Haurie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 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 attractors, the limit control problem can be given an interpretation related to a decomposition approach.

Original languageEnglish
Pages (from-to)179-190
Number of pages12
JournalIEEE Transactions on Automatic Control
Volume46
Issue number2
DOIs
Publication statusPublished - Feb 2001
Externally publishedYes

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