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first-passage time OF QUASI-NON-INTEGRABLE-HAMILTONIAN SYSTEM

Acta Mechanica Sinica 2000年第2期16卷 183-192页

作者：甘春标徐博侯 Department of Mechanics. Zhejiang University Hangzhou China 310027

Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure.

关键词： Hamiltonian system non-integrable stochastic averaging method Pontryagin equation first-passage time

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

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Acta Mechanica Sinica 2007年第4期23卷 437-444页

作者： Maolin Deng Weiqiu Zhu Department of Mechanics,State Key Laboratory of Fluid Power Transmission and Control,Zhejiang University,Hangzhou 310027,China Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou China

Abstract 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 maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The final dynamical programming equations for these control problems 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 dynamical programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illustrate the application and effectiveness of the proposed control strategy.

关键词： Nonlinear stochastic system first-passage time Reliability Stochastic control Dynamical programming

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