Stochastic Optimal Control for First-Passage Failure of Nonlinear Oscillators with Multi-Degrees-of-Freedom

doi:10.1007/s12204-013-1428-8

上海交通大学学报（英文版） ›› 2013, Vol. 18 ›› Issue (5): 577-582.doi: 10.1007/s12204-013-1428-8

Stochastic Optimal Control for First-Passage Failure of Nonlinear Oscillators with Multi-Degrees-of-Freedom

GAO Yang-yan (高阳艳), WU Yong-jun* (吴勇军)

(Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China)

出版日期:2013-10-31 发布日期:2013-12-05
通讯作者: WU Yong-jun(吴勇军) E-mail:yj.wu@sjtu.edu.cn

Stochastic Optimal Control for First-Passage Failure of Nonlinear Oscillators with Multi-Degrees-of-Freedom

GAO Yang-yan (高阳艳), WU Yong-jun* (吴勇军)

(Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China)

Online:2013-10-31 Published:2013-12-05
Contact: WU Yong-jun(吴勇军) E-mail:yj.wu@sjtu.edu.cn

摘要/Abstract

摘要： 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.

关键词: stochastic averaging method, dynamical programming principle, backward Kolmogorov (BK) equation, Pontryagin equation

Abstract: 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.

Key words: stochastic averaging method, dynamical programming principle, backward Kolmogorov (BK) equation, Pontryagin equation

中图分类号:

O 322

GAO Yang-yan (高阳艳), WU Yong-jun* (吴勇军). Stochastic Optimal Control for First-Passage Failure of Nonlinear Oscillators with Multi-Degrees-of-Freedom[J]. 上海交通大学学报（英文版）, 2013, 18(5): 577-582.

GAO Yang-yan (高阳艳), WU Yong-jun* (吴勇军). Stochastic Optimal Control for First-Passage Failure of Nonlinear Oscillators with Multi-Degrees-of-Freedom[J]. Journal of shanghai Jiaotong University (Science), 2013, 18(5): 577-582.

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Stochastic Optimal Control for First-Passage Failure of Nonlinear Oscillators with Multi-Degrees-of-Freedom

Stochastic Optimal Control for First-Passage Failure of Nonlinear Oscillators with Multi-Degrees-of-Freedom

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