Response of quasi-integrable Hamiltonian systems with delayed feedback bang–bang control

被引：0
作者：
W. Q. Zhu
Z. H. Liu
机构：
[1] Zhejiang University,Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control
[2] Zhejiang University,Department of Physics
来源：
Nonlinear Dynamics | 2007年 / 49卷
关键词：
Delayed feedback bang–bang control; Gaussian white noise; Quasi-integrable Hamiltonian system; Stationary solution; Stochastic averaging method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The response of quasi-integrable Hamiltonian systems with delayed feedback bang–bang control subject to Gaussian white noise excitation is studied by using the stochastic averaging method. First, a quasi-Hamiltonian system with delayed feedback bang–bang control subjected to Gaussian white noise excitation is formulated and transformed into the Itô stochastic differential equations for quasi-integrable Hamiltonian system with feedback bang–bang control without time delay. Then the averaged Itô stochastic differential equations for the later system are derived by using the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution of the averaged Fokker–Plank–Kolmogorov (FPK) equation associated with the averaged Itô equations is obtained for both nonresonant and resonant cases. Finally, two examples are worked out in detail to illustrate the application and effectiveness of the proposed method and the effect of time delayed feedback bang–bang control on the response of the systems.
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页码：31 / 47
页数：16
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