Stochastic optimal time-delay control of quasi-integrable Hamiltonian systems |
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Institution: | 1. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, PR China;2. Department of Civil Engineering, Xiamen University, Xiamen 361005, PR China |
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Abstract: | 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. |
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