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Stochastic optimal bounded control of MDOF quasi nonintegrable-Hamiltonian systems with actuator saturation

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Abstract

A new bounded optimal control strategy for multi-degree-of-freedom (MDOF) quasi nonintegrable-Hamiltonian systems with actuator saturation is proposed. First, an n-degree-of-freedom (n-DOF) controlled quasi nonintegrable-Hamiltonian system is reduced to a partially averaged Itô stochastic differential equation by using the stochastic averaging method for quasi nonintegrable-Hamiltonian systems. Then, a dynamical programming equation is established by using the stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang–bang control is derived. Finally, the response of the optimally controlled system is predicted by solving the Fokker–Planck–Kolmogorov (FPK) equation associated with the fully averaged Itô equation. An example of two controlled nonlinearly coupled Duffing oscillators is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and that chattering is reduced significantly compared with the bang–bang control strategy.

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Authors and Affiliations

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

    Ronghua Huan & Weiqiu Zhu

  2. School of Information Science and Engineering, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Yongjun Wu

Authors
  1. Ronghua Huan
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  2. Yongjun Wu
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  3. Weiqiu Zhu
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Correspondence to Weiqiu Zhu.

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Huan, R., Wu, Y. & Zhu, W. Stochastic optimal bounded control of MDOF quasi nonintegrable-Hamiltonian systems with actuator saturation. Arch Appl Mech 79, 157–168 (2009). https://doi.org/10.1007/s00419-008-0218-5

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  • DOI: https://doi.org/10.1007/s00419-008-0218-5

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