A minimax optimal control strategy for uncertain quasi-Hamiltonian systems |
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| Authors: | Yong Wang Zu-guang Ying and Wei-qiu Zhu |
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| Institution: | (1) Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China |
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| Abstract: | A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged It6 stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs (HJI) equation. Numerical results for a controlled and stochastically excited Duffing oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy. |
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| Keywords: | Nonlinear quasi-Hamiltonian system Minimax optimal control Stochastic excitation Uncertain disturbance Stochastic averaging Stochastic differential game |
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