First-passage failure and optimal control of stochastic Rayleigh oscillator

The first-passage failure and optimal control of stochastic Rayleigh oscillator are studied in this paper. An averaged Itô stochastic differential Equation of the stochastic system is reduced by using the stochastic averaging method. A backward Kolmogorov Equation governing the conditional reliability function of first passage failure is then established. The conditional reliability function and the conditional probability density are also obtained by solving the backward Kolmogorov Equation with boundary conditions. Finally, an optimal control law of this system is obtained.