一类内共振非线性随机振动系统的可靠性控制

本文研究了一类随机激励的多自由度非线性内共振拟可积哈密顿系统的首次穿越可靠性的最优控制问题。基于随机平均法与动态规划原理，得到了最优控制系统的It？随机微分方程，建立了最优控制系统条件可靠性函数满足的后向Kolmogorov方程及平均首次穿越时间满足的Pontryagin方程。通过具体的算例，结合Monte Carlo数值模拟验证了理论方法的有效性。
Abstract：Here, the optimal control problem for first-passage reliability of a class of randomly excited multi-DOF nonlinear quasi-integrable Hamiltonian systems with internal resonance was investigated.Based on the stochastic averaging method and dynamic programming principle, the It stochastic differential equations of the optimally controlled system were obtained.Then the backward Kolmogorov equation governing conditional reliability function and the Pontryagin equation governing the mean first-passage time were established.An illustrative numerical example was given.The validity of the theoretical method was verified by Monte Carlo digital simulation.