Stochastic stabilization of quasi integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitation

作     者：Liu, Weiyan Yin, Xunru Guo, Zhongjin Jiang, Shan 

作者机构：Taishan Univ Sch Math & Stat Tai An 271000 Peoples R China 

出 版 物：《PROBABILISTIC ENGINEERING MECHANICS》 (Probab Eng Mech)

年 卷 期：2025年第79卷

核心收录：

学科分类：08[工学] 0714[理学-统计学（可授理学、经济学学位）] 0802[工学-机械工程] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Shandong Provincial Natural Science Foundation of China [ZR2021MA086, ZR2014AQ028] National Natural Science Foundation of China Tai 'an City science and technology innovation development, China [2023GX006] Project of Shandong Province Higher Education Science and Technology, China Program [J15LI14] 

主　　题：Stochastic stabilization Quasi integrable and non-resonant Hamiltonian system Asymptotic Lyapunov stability with probability one Dynamical programming The largest Lyapunov exponent Stochastic averaging 

摘      要：A stochastic stabilization control strategy is proposed for multi-degree-of-freedom (MDOF) quasi integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitation. At first, the averaged It stochastic differential equations (SDEs) for controlled first integrals are derived from the system motion equations by using the stochastic averaging method. Second, the dynamical programming equation of the averaged system with undetermined cost function is established based on the dynamical programming principle. The optimal control law is given through solving the dynamical programming equation. Third, the asymptotic Lyapunov stability with probability one of the controlled system is analyzed approximately by evaluating the largest Lyapunov exponent of the averaged system. Finally, the cost function and optimal control forces are determined based on the requirement of stabilizing the system. An example is delivered to illustrate the application and effectiveness of the proposed stochastic stabilization control strategy.