IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v25y2005i5p1221-1228.html
   My bibliography  Save this article

Stochastic optimal control of first-passage failure for coupled Duffing–van der Pol system under Gaussian white noise excitations

Author

Listed:
  • Li, Wei
  • Xu, Wei
  • Zhao, Junfeng
  • Ma, Shaojuan

Abstract

In this paper, the stochastic averaging method of quasi-non-integrable-Hamiltonian systems is applied to Duffing–van der Pol system to obtain partially averaged Ito stochastic differential equations. On the basis of the stochastic dynamical programming principle and the partially averaged Ito equation, dynamical programming equations for the reliability function and the mean first-passage time of controlled system are established. Then a non-linear stochastic optimal control strategy for coupled Duffing–van der Pol system subject to Gaussian white noise excitation is taken for investigating feedback minimization of first-passage failure. By averaging the terms involving control forces and replacing control forces by the optimal ones, the fully averaged Ito equation is derived. Thus, the feedback minimization for first-passage failure of controlled system can be obtained by solving the final dynamical programming equations. Numerical results for first-passage reliability function and mean first-passage time of the controlled and uncontrolled systems are compared in illustrative figures to show effectiveness and efficiency of the proposed method.

Suggested Citation

  • Li, Wei & Xu, Wei & Zhao, Junfeng & Ma, Shaojuan, 2005. "Stochastic optimal control of first-passage failure for coupled Duffing–van der Pol system under Gaussian white noise excitations," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1221-1228.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:5:p:1221-1228
    DOI: 10.1016/j.chaos.2004.11.066
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905000202
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2004.11.066?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.

    Citations

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


    Cited by:

    1. Jing, Zhujun & Huang, Jicai & Deng, Jin, 2007. "Complex dynamics in three-well duffing system with two external forcings," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 795-812.
    2. Li, Wei & Li, Jiaorui & Chen, Weisheng, 2012. "The reliability of a stochastically complex dynamical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(13), pages 3556-3565.
    3. Li, Wei & Xu, Wei & Zhao, Junfeng & Jin, Yanfei, 2006. "First-passage problem for strong nonlinear stochastic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 414-421.

    More about this item

    Statistics

    Access and download statistics

    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:eee:chsofr:v:25:y:2005:i:5:p:1221-1228. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.