Stochastic Stabilization of Quasi-Partially Integrable Hamiltonian Systems by Using Lyapunov Exponent

被引：0

作者：

W. Q. Zhu

Z. L. Huang

机构：

[1] Zhejiang University,Department of Mechanics

来源：

Nonlinear Dynamics | 2003年 / 33卷

关键词：

nonlinear system; stochastic excitation; stochastic averaging; stochastic optimal control; dynamical programming; stochastic stabilization; Lyapunov exponent;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A procedure for designing a feedback control to asymptoticallystabilize, with probability one, a quasi-partially integrableHamiltonian system is proposed. First, the averaged stochasticdifferential equations for controlled r first integrals are derived fromthe equations of motion of a given system by using the stochasticaveraging method for quasi-partially integrable Hamiltonian systems.Second, a dynamical programming equation for the ergodic control problemof the averaged system with undetermined cost function is establishedbased on the dynamical programming principle. The optimal control law isderived from minimizing the dynamical programming equation with respectto control. Third, the asymptotic stability with probability one of theoptimally controlled system is analyzed by evaluating the maximalLyapunov exponent of the completely averaged Itô equations for the rfirst integrals. Finally, the cost function and optimal control forces aredetermined by the requirements of stabilizing the system. An example isworked out in detail to illustrate the application of the proposedprocedure and the effect of optimal control on the stability of thesystem.

引用

页码：209 / 224

页数：15

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