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On asymptotic optimization of a class of nonlinear stochastic hybrid systems

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  • Peng Shi
  • Eitan Altman
  • Vladimir Gaitsgory

Abstract

We consider the problem of control for continuous time stochastic hybrid systems in finite time horizon. The systems considered are nonlinear: the state evolution is a nonlinear function of both the control and the state. The control parameters change at discrete times according to an underlying controlled Markov chain which has finite state and action spaces. The objective is to design a controller which would minimize an expected nonlinear cost of the state trajectory. We show using an averaging procedure, that the above minimization problem can be approximated by the solution of some deterministic optimal control problem. This paper generalizes our previous results obtained for systems whose state evolution is linear in the control. Copyright Physica-Verlag 1998

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:47:y:1998:i:2:p:289-315
    DOI: 10.1007/BF01194402
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    Cited by:

    1. Ilaria Brunetti & Vladimir Gaitsgory & Eitan Altman, 2017. "On Nonzero-Sum Game Considered on Solutions of a Hybrid System with Frequent Random Jumps," Dynamic Games and Applications, Springer, vol. 7(3), pages 386-401, September.
    2. 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.
    3. S. P. Sethi & H. Yan & H. Zhang & Q. Zhang, 2002. "Optimal and Hierarchical Controls in Dynamic Stochastic Manufacturing Systems: A Survey," Manufacturing & Service Operations Management, INFORMS, vol. 4(2), pages 133-170.

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