A minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems |
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Authors: | J Feng ZG Ying WQ Zhu |
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Institution: | Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China |
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Abstract: | A stochastic minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems is proposed. First, the stochastic optimal control problem of a partially observable nonlinear uncertain quasi-Hamiltonian system is converted into that of a completely observable linear uncertain system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by a minimax optimal control strategy based on stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs (HJI) equation. As an example, the stochastic minimax optimal control of a partially observable Duffing–van der Pol oscillator with uncertain disturbances is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy. |
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