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

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  • 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
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    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.
    4. Guan, Yu & Li, Wei & Kozak, Drazan & Zhao, Junfeng, 2024. "Response and reliability analysis of a nonlinear VEH systems with FOPID controller by improved stochastic averaging method and LBFNN algorithm," Reliability Engineering and System Safety, Elsevier, vol. 249(C).

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