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

Eitan Altman*, Vladimir Gaitsgory

*Corresponding author for this work

Research output: Contribution to journalArticle

18 Citations (Scopus)

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 e 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.

Original languageEnglish
Pages (from-to)2070-2085
Number of pages16
JournalSIAM Journal on Control and Optimization
Volume35
Issue number6
Publication statusPublished - Nov 1997
Externally publishedYes

Keywords

  • Asymptotic optimality
  • Averaging
  • Hybrid stochastic systems
  • Markov decision processes
  • Nonlinear dynamics

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