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Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle

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Abstract

A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with uncertain parameters. Then, the stochastic Hamiltonian system for minimax optimal control with a given performance index is established based on the stochastic maximum principle. The worst disturbances are determined by minimizing the Hamiltonian function, and the worst-case optimal controls are obtained by maximizing the minimal Hamiltonian function. The differential equation for adjoint process as a function of system energy is derived from the adjoint equation by using the Itô differential rule. Finally, two examples of controlled uncertain quasi-Hamiltonian systems are worked out to illustrate the application and effectiveness of the proposed control strategy.

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Acknowledgments

This study was supported by the National Natural Science Foundation of China under Grant Nos. 10932009, 11072212, 11072215 and 11272279.

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Authors and Affiliations

  1. Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    R. C. Hu, Z. G. Ying & W. Q. Zhu

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  1. R. C. Hu
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  2. Z. G. Ying
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  3. W. Q. Zhu
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Correspondence to Z. G. Ying.

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Hu, R.C., Ying, Z.G. & Zhu, W.Q. Stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems using stochastic maximum principle. Struct Multidisc Optim 49, 69–80 (2014). https://doi.org/10.1007/s00158-013-0958-x

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  • DOI: https://doi.org/10.1007/s00158-013-0958-x

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