摘要
近几年来,笔者提出与发展了随机激励的耗散的哈密顿系统理论,包括精确平稳解、等效非线性系统法、拟哈密顿系统随机平均法、拟哈密顿系统的随机稳定性与随机分岔、首次穿越损坏分析方法及非线性随机最优控制策略,从而构成了一个非线性随机动力学与控制的哈密顿理论框架．本文简要介绍这一理论框架．
In recent years, we proposed and developed a theory of stochastically excited anddissipated Hamiltonian systems, including exact stationary solutions, equivalent nonlinear system method,stochastic averaging method for quasi Hamiltonian systems, and approaches to stochastic stability, stochasticbifurcation, first passage failure and nonlinear stochastic optimal control of quasi Hamiltonian systems, whichconstitute a Hamiltonian framework of nonlinear stochastic dynamics and control. In the present paper thisframework is briefly introduced.
出处
《力学与实践》
CSCD
北大核心
2002年第3期1-9,29,共10页
Mechanics in Engineering
基金
国家自然科学基金项目(19972059
10002015)资助.
关键词
哈密顿理论
非线性系统
随机响应
随机稳定性
随机分岔
nonlinear system, stochastic response, stochastic stability, stochastic bifurcation, first-passagefailure, reliability, stochastic optimal control
