Ergodic Control of a Singularly Perturbed Markov Process in Discrete Time with General State and Compact Action Spaces

Journal Article · Sun Nov 15 04:00:00 EST 1998 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459900091· OSTI ID:21064293

Bielecki, T R ^[1]; Stettner, L ^[2]

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1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607 (United States)
2. Institute of Mathematics, Polish Academy of Sciences, 00-950 Warsaw (Poland)

Ergodic control of singularly perturbed Markov chains with general state and compact action spaces is considered. A new method is given for characterization of the limit of invariant measures, for perturbed chains, when the perturbation parameter goes to zero. It is also demonstrated that the limit control principle is satisfied under natural ergodicity assumptions about controlled Markov chains. These assumptions allow for the presence of transient states, a situation that has not been considered in the literature before in the context of control of singularly perturbed Markov processes with long-run-average cost functionals.

• OSTI ID: 21064293
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 38; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CONTROL THEORY
FUNCTIONALS
MARKOV PROCESS
MATHEMATICAL SPACE
PERTURBATION THEORY
TOPOLOGY