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Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains

Author

Listed:
  • G. Badowski

    (University of Maryland at College Park)

  • G. Yin

    (Wayne State University)

  • Q. Zhang

    (University of Georgia)

Abstract

This work is devoted to near-optimal controls of large-scale discrete-time nonlinear dynamic systems driven by Markov chains; the underlying problem is to minimize an expected cost function. Our main goal is to reduce the complexity of the underlying systems. To achieve this goal, discrete-time control models under singularly-perturbed Markov chains are introduced. Using a relaxed control representation, our effort is devoted to finding near-optimal controls. Lumping the states in each irreducible class into a single state gives rise to a limit system. Applying near-optimal controls of the limit system to the original system, near-optimal controls of the original system are derived.

Suggested Citation

  • G. Badowski & G. Yin & Q. Zhang, 2003. "Near-Optimal Controls of Discrete-Time Dynamic Systems Driven by Singularly-Perturbed Markov Chains," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 131-166, January.
    • Handle: RePEc:spr:joptap:v:116:y:2003:i:1:d:10.1023_a:1022166304069
    DOI: 10.1023/A:1022166304069
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    References listed on IDEAS

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    1. Peng Shi & Eitan Altman & Vladimir Gaitsgory, 1998. "On asymptotic optimization of a class of nonlinear stochastic hybrid systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(2), pages 289-315, June.
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