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Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

Acta Mechanica Sinica 2007年第3期23卷 311-319页

作者： Ronghua Huan Maolin Deng Weiqiu Zhu Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang UniversityHangzhou 310027 China

In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged It^↑o stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged It^↑o equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged It^↑o equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

关键词： Nonlinear system stochastic excitation stochastic averaging Optimal control Dynamical programming

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