IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v63y2006i3p443-460.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-005-0024-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-005-0024-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Evgueni Gordienko & Enrique Lemus-Rodríguez & Raúl Montes-de-Oca, 2008. "Discounted cost optimality problem: stability with respect to weak metrics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 77-96, August.
    3. Arnoud V. den Boer & Bert Zwart, 2015. "Dynamic Pricing and Learning with Finite Inventories," Operations Research, INFORMS, vol. 63(4), pages 965-978, August.
    4. Hong Chen & Murray Zed Frank, 2022. "Equilibrium Defaultable Corporate Debt and Investment," Papers 2202.05885, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:63:y:2006:i:3:p:443-460. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.