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

IF 3.5 3区工程技术 Q2 ENGINEERING, MECHANICAL

Probabilistic Engineering Mechanics Pub Date : 2025-01-01 DOI:10.1016/j.probengmech.2025.103733

Weiyan Liu, Xunru Yin, Zhongjin Guo, Shan Jiang

{"title":"Stochastic stabilization of quasi integrable and non-resonant Hamiltonian systems under combined Gaussian and Poisson white noise excitation","authors":"Weiyan Liu, Xunru Yin, Zhongjin Guo, Shan Jiang","doi":"10.1016/j.probengmech.2025.103733","DOIUrl":null,"url":null,"abstract":"<div><div>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 Itô 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.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103733"},"PeriodicalIF":3.5000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probabilistic Engineering Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0266892025000050","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}

引用次数: 0

Abstract

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 Itô 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.

查看原文本刊更多论文

高斯和泊松白噪声联合激励下拟可积非谐振哈密顿系统的随机镇定

针对高斯白噪声和泊松白噪声联合激励下的多自由度拟可积非谐振哈密顿系统，提出了一种随机镇定控制策略。首先，利用随机平均法从系统运动方程中导出受控第一积分的平均Itô随机微分方程（SDEs）。其次，根据动态规划原理，建立了成本函数未定的平均系统的动态规划方程；通过求解动态规划方程，给出了最优控制律。第三，通过求平均系统的最大Lyapunov指数，近似分析了被控系统的概率为1的渐近Lyapunov稳定性。最后，根据稳定系统的要求，确定成本函数和最优控制力。最后通过一个实例说明了所提出的随机稳定控制策略的应用和有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Probabilistic Engineering Mechanics 工程技术-工程：机械

CiteScore

3.80

自引率

15.40%

发文量

审稿时长

13.5 months

期刊介绍： This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.