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Adaptive control of stochastic systems with unknown disturbance distribution: discounted criteria

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  • Nadine Hilgert
  • J. Minjárez-Sosa

Abstract

We consider a class of discrete-time stochastic control systems, with Borel state and action spaces, and possibly unbounded costs. The processes evolve according to the equation x t +1 =F(x t , a t , ξ t ), t=0, 1, ..., where the ξ t are i.i.d. random vectors whose common distribution is unknown. Assuming observability of {ξ t }, we use the empirical estimator of its distribution to construct adaptive policies which are asymptotically discounted cost optimal . Copyright Springer-Verlag Berlin Heidelberg 2006

Suggested Citation

  • Nadine Hilgert & J. Minjárez-Sosa, 2006. "Adaptive control of stochastic systems with unknown disturbance distribution: discounted criteria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 443-460, July.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:3:p:443-460
    DOI: 10.1007/s00186-005-0024-6
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    References listed on IDEAS

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    1. J. A. E. E. van Nunen & J. Wessels, 1978. "Note--A Note on Dynamic Programming with Unbounded Rewards," Management Science, INFORMS, vol. 24(5), pages 576-580, January.
    2. Evgueni I. Gordienko & J. Adolfo Minjárez-Sosa, 1998. "Adaptive control for discrete-time Markov processes with unbounded costs: Average criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(1), pages 37-55, September.
    3. Nadine Hilgert & J. Adolfo Minjárez-Sosa, 2001. "Adaptive policies for time-varying stochastic systems under discounted criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(3), pages 491-505, December.
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    Cited by:

    1. J. Minjárez-Sosa, 2015. "Markov control models with unknown random state–action-dependent discount factors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 743-772, October.
    2. Beatris Adriana Escobedo-Trujillo & José Daniel López-Barrientos & Carmen Geraldi Higuera-Chan & Francisco Alejandro Alaffita-Hernández, 2023. "Robust Statistic Estimation in Constrained Optimal Control Problems of Pollution Accumulation (Part II: Markovian Switchings)," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    3. Beatris Adriana Escobedo-Trujillo & José Daniel López-Barrientos & Carmen Geraldi Higuera-Chan & Francisco Alejandro Alaffita-Hernández, 2023. "Robust Statistic Estimation of Constrained Optimal Control Problems of Pollution Accumulation (Part I)," Mathematics, MDPI, vol. 11(4), pages 1-19, February.

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