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

ISSN号：0567-7718
期刊名称：《力学学报：英文版》
时间：0
分类：O3[理学—力学]
作者机构：[1] Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027, China
相关基金：The project supported by the National Natural Science Foundation of China （10332030） and the Special Fund for Doctor Programs in Institutions of Higher Learning of China （20060335125）.

关键词：非线性随机系统, 第一通过时间, 可靠性, 随机控制, Nonlinear stochastic system, First-passage time, Reliability, Stochastic control, Dynamical programming

中文摘要：

为最小化伪 integrable Hamiltonian 系统(点亮水坝砰和弱随机的刺激的 multi-degree-of-freedom integrable Hamiltonian 系统题目) 的第一经过的失败的非线性的随机的最佳的控制策略被建议。为一个控制伪 integrable Hamiltonian 系统的运动的方程被使用随机的平均方法归结为一套平均 Itô 随机的微分方程。然后，动态编程方程和他们的联系边界和期末考试为可靠性的最大化的控制问题预定条件，吝啬的第一经过的时间被提出。最佳的控制法律从动态编程方程和控制限制被导出。为这些控制问题的最后的动态编程方程被决定，他们到管理有条件的可靠性的向后的 Kolmogorov 方程的关系工作，管理吝啬的第一经过的时间的 Pontryagin 方程独立被建立。有条件的可靠性功能和控制系统的吝啬的第一经过的时间被解决最后的动态编程方程和 Pontryagin 方程获得。一个例子被举说明建议控制策略的应用程序和有效性。

英文摘要：

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.

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