First-passage failure minimization of stochastic Duffing–Rayleigh–Mathieu system

Combing stochastic averaging method with dynamical programming principle, we propose a new stochastic optimal control strategy for minimizing first-passage failure of Duffing–Rayleigh–Mathieu system under wide-band colored noise excitations. The motion equation of the controlled system is reduced to homogeneous diffusion processes by stochastic averaging. The optimal control law is determined according to dynamical programming equation and the control constraint. The diffusion process method for first-passage problem is applied. It is shown that the reliability of the system can be improved remarkably by the proposed strategy. The validity of the proposed method is confirmed by Monte Carlo simulation.