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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2008, Vol. 9 Issue (7): 950-954    DOI: 10.1631/jzus.A0820014
Applied Mechanics     
A minimax optimal control strategy for uncertain quasi-Hamiltonian systems
Yong WANG, Zu-guang YING, Wei-qiu ZHU
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 Itô 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.

Key words： Nonlinear quasi-Hamiltonian system      Minimax optimal control      Stochastic excitation      Uncertain disturbance      Stochastic averaging      Stochastic differential game     
Received: 05 January 2008     
CLC:  TP13  
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Zu-guang YING
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Yong WANG, Zu-guang YING, Wei-qiu ZHU. A minimax optimal control strategy for uncertain quasi-Hamiltonian systems. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(7): 950-954.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A0820014     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2008/V9/I7/950

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