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Stochastic minimax optimal time-delay state feedback control of uncertain quasi-integrable Hamiltonian systems. (English) Zbl 1323.70084

Summary: A stochastic minimax optimal time-delay state feedback control strategy for uncertain quasi-integrable Hamiltonian systems is proposed. First, a stochastic optimal state feedback control problem of uncertain quasi-integrable Hamiltonian system with time delay in feedback control subjected to Gaussian white noise is formulated. Then the time-delayed state feedback control forces are approximated by the control forces without time delay, and the original problem is converted into a stochastic optimal state feedback control problem of an uncertain system without time delay. After that, by following a procedure based on the stochastic averaging method and stochastic differential game, the worst-case disturbances and the optimal controls are obtained from solving a Hamiltonian-Jacobi-Isaacs equation. As an example, the stochastic minimax optimal state feedback control of a Duffing oscillator with parametric disturbances and time-delayed feedback control is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.

MSC:

70Q05 Control of mechanical systems
70H08 Nearly integrable Hamiltonian systems, KAM theory
93B52 Feedback control
93E20 Optimal stochastic control
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