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On asymptotic optimization of a class of nonlinear stochastic hybrid systems
Authors:Peng Shi  Eitan Altman  Vladimir Gaitsgory
Affiliation:(1) Centre for Industrial and Applied Mathematics, School of Mathematics, The University of South Australia, 5095 SA, Australia;(2) INRIA, 2004 Route des Lucioles, BP93, 06902 Sophia Antipolis Cedex, France;(3) Centre for Industrial and Applied Mathematics, School of Mathematics, The University of South Australia, 5095 SA, Australia
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.This work is supported by the Australian Research Council. All correspondence should be directed to the first author.
Keywords:Hybrid stochastic systems  Markov decision processes  nonlinear systems
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