Monte Carlo TD(λ)-methods for the optimal control of discrete-time Markovian jump linear systems

  • Authors:

  • Oswaldo L. V. Costa;Julio C. C. Aya

  • Affiliations:

  • Departamento de Engenharia de Telecomunicaçíes e Controle, Escola Politécnica da Universidade de São Paulo, CEP: 05508 900 São Paulo SP Brazil;Departamento de Engenharia de Telecomunicaçíes e Controle, Escola Politécnica da Universidade de São Paulo, CEP: 05508 900 São Paulo SP Brazil

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2002

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Abstract

In this paper, we present an iterative technique based on Monte Carlo simulations for deriving the optimal control of the infinite horizon linear regulator problem of discrete-time Markovian jump linear systems for the case in which the transition probability matrix of the Markov chain is not known. We trace a parallel with the theory of TD(@l) algorithms for Markovian decision processes to develop a TD(@l) like algorithm for the optimal control associated to the maximal solution of a set of coupled algebraic Riccati equations (CARE). It is assumed that either there is a sample of past observations of the Markov chain that can be used for the iterative algorithm, or it can be generated through a computer program. Our proofs rely on the spectral radius of the closed loop operators associated to the mean square stability of the system being less than 1.