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

Ergodic Control of a Singularly Perturbed Markov Process in Discrete Time with General State and... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 1998 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900091
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2090

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