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Singular perturbations and asymptotic analysis in control systems
- Publisher
- Springer Journals
- 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
- DOI
- 10.1007/s002459900091
- Publisher site
- See Article on Publisher Site
Abstract
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 Optimization – Springer Journals
Published: Dec 1, 1998
Keywords: Key words. Markov process, Invariant measure, Singular perturbation, Ergodic control, Limit control principle. AMS Classification. Primary 60J05, 47A55, Secondary 90C40.