IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v165y2015i1d10.1007_s10957-014-0612-9.html
   My bibliography  Save this article

Optimal Control Problems for Lipschitz Dissipative Systems with Boundary-Noise and Boundary-Control

Author

Listed:
  • Desheng Yang

    (Central South University)

Abstract

This paper studies the infinite-horizon optimal control problems for Lipschitz dissipative systems with boundary-control and boundary-noise of Neumann type. By introducing Sobolev spaces based on the invariant measure and using the m-dissipativity of the Kolmogorov operator, corresponding to the uncontrolled system, we prove the existence of a unique mild solution of the associated stationary Hamilton–Jacobi–Bellman equation under the general cost functional and obtain the optimal control in the feedback law.

Suggested Citation

  • Desheng Yang, 2015. "Optimal Control Problems for Lipschitz Dissipative Systems with Boundary-Noise and Boundary-Control," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 14-29, April.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0612-9
    DOI: 10.1007/s10957-014-0612-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-014-0612-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-014-0612-9?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. Goldys, B. & Gozzi, F., 2006. "Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: approach," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1932-1963, 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. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.

    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. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    2. F. Gozzi & C. Marinelli & S. Savin, 2009. "On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 291-321, August.
    3. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    4. Filippo de Feo & Salvatore Federico & Andrzej 'Swik{e}ch, 2023. "Optimal control of stochastic delay differential equations and applications to path-dependent financial and economic models," Papers 2302.08809, arXiv.org.
    5. Fabbri, G. & Russo, F., 2017. "HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition," Working Papers 2017-07, Grenoble Applied Economics Laboratory (GAEL).

    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:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0612-9. 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.