Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems

• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2007,（4）
• 页码范围: 437-444
• 页数: 8页
• 语种: 英文

摘要

A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems (multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations) is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximiza-tion of reliability and mean first-passage time are formulated.The optimal control law is derived from the dynamical pro-gramming equations and the control constraints. The final dynamical programming equations for these control prob-lems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynami-cal programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illus-trate the application and effectiveness of the proposed control strategy.