Stochastic optimal control for first-passage failure of nonlinear oscillators with multi-degrees-of-freedom

To enhance the reliability of the stochastically excited structure, it is significant to study the problem of stochastic optimal control for minimizing first-passage failure. Combining the stochastic averaging method with dynamical programming principle, we study the optimal control for minimizing first-passage failure of multidegrees-of-freedom (MDoF) nonlinear oscillators under Gaussian white noise excitations. The equations of motion of the controlled system are reduced to time homogenous diffusion processes by stochastic averaging. The optimal control law is determined by the dynamical programming equations and the control constraint. The backward Kolmogorov (BK) equation and the Pontryagin equation are established to obtain the conditional reliability function and mean first-passage time (MFPT) of the optimally controlled system, respectively. An example has shown that the proposed control strategy can increase the reliability and MFPT of the original system, and the mathematical treatment is also facilitated. © Shanghai Jiaotong University and Springer-Verlag Berlin Heidelberg 2013.