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Stochastic fractional optimal control of quasi-integrable Hamiltonian system with fractional derivative damping

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Abstract

A stochastic fractional optimal control strategy for quasi-integrable Hamiltonian systems with fractional derivative damping is proposed. First, equations of the controlled system are reduced to a set of partially averaged It\(\hat{o}\) stochastic differential equations for the energy processes by applying the stochastic averaging method for quasi-integrable Hamiltonian systems and a stochastic fractional optimal control problem (FOCP) of the partially averaged system for quasi-integrable Hamiltonian system with fractional derivative damping is formulated. Then the dynamical programming equation for the ergodic control of the partially averaged system is established by using the stochastic dynamical programming principle and solved to yield the fractional optimal control law. Finally, an example is given to illustrate the application and effectiveness of the proposed control design procedure.

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Acknowledgements

The work reported in this paper was supported by the National Natural Science Foundation of China under Grant Nos. 10932009, 11072212, and 11002059, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20103501120003, the Fujian Province Natural Science Foundation of China under Grant No. 2010J05006, and the Fundamental Research Funds for Huaqiao University under Grant No. JB-SJ1010.

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Authors and Affiliations

  1. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China

    F. Hu & W. Q. Zhu

  2. College of Civil Engineering, Huaqiao University, 362021, Xiamen, China

    L. C. Chen

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  1. F. Hu
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  2. W. Q. Zhu
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  3. L. C. Chen
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Correspondence to W. Q. Zhu.

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Hu, F., Zhu, W.Q. & Chen, L.C. Stochastic fractional optimal control of quasi-integrable Hamiltonian system with fractional derivative damping. Nonlinear Dyn 70, 1459–1472 (2012). https://doi.org/10.1007/s11071-012-0547-3

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