Stochastic optimal time-delay control of quasi-integrable Hamiltonian systems

Ju Feng, Wei-Qiu Zhu, Zhong-Hua Liu

Research output: Contribution to journalJournal articleResearchpeer-review


A nonlinear stochastic optimal time-delay control strategy for quasi-integrable Hamiltonian systems is proposed. First, a stochastic optimal control problem of quasi-integrable Hamiltonian system with time-delay in feedback control subjected to Gaussian white noise is formulated. Then, the time-delayed feedback control forces are approximated by the control forces without time-delay and the original problem is converted into a stochastic optimal control problem without time-delay. After that, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. As an example, the stochastic time-delay optimal control of two coupled van der Pol oscillators under stochastic excitation is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.
Original languageEnglish
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number8
Pages (from-to)2978-2984
Publication statusPublished - 2011
Externally publishedYes


  • Stochastic optimal control
  • Time-delay
  • Quasi-integrable Hamiltonian system
  • Stochastic averaging

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