Asymptotic optimization of a nonlinear hybrid system governed by a Markov decision process

Asymptotic optimization of a nonlinear hybrid system governed by a Markov decision process

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Article ID: iaor19981801
Volume: 35
Issue: 6
Start Page Number: 2070
End Page Number: 2085
Publication Date: Nov 1997
Journal: SIAM Journal on Control and Optimization
Authors: ,
Keywords: programming: dynamic, markov processes
Abstract:

We consider in this paper a continuous time stochastic hybrid control system with finite time horizon. The objective is to minimize a nonlinear function of the state trajectory. The state evolves according to a nonlinear dynamics. The parameters of the dynamics of the system may change at discrete times lϵ, l = 0, 1, ..., according to a controlled Markov chain which has finite state and action spaces. Under the assumption that ϵ is a small parameter, we justify an averaging procedure allowing us to establish that our problem can be approximated by the solution of some deterministic optimal control problem.

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