{"title":"Backstepping control for stochastic strict-feedback systems with Lévy noise","authors":"K. Mathiyalagan, T. Elizabeth Jeyanthi","doi":"10.1016/j.chaos.2025.116241","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, a class of nonlinear strict-feedback continuous time stochastic jump diffusion system (SJDS) driven by Lévy noise is considered. The aim of this work is to design control function for the system to obtain global asymptotic stability at the origin in probability. Backstepping method is used to design the robust stabilizing control function. Also, quartic form Lyapunov functional is utilized to stabilize the system with high amplified energy. Fourth-moment exponential stability conditions for the closed loop system are derived using It<span><math><mover><mrow><mi>o</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>’s differential. Further, numerical examples are presented to show the applications of the theoretical results to physical systems. The effectiveness of the designed control function in the process of convergence of error vector are depicted in the form of error covariance matrices in the simulation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"195 ","pages":"Article 116241"},"PeriodicalIF":5.3000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077925002541","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
In this paper, a class of nonlinear strict-feedback continuous time stochastic jump diffusion system (SJDS) driven by Lévy noise is considered. The aim of this work is to design control function for the system to obtain global asymptotic stability at the origin in probability. Backstepping method is used to design the robust stabilizing control function. Also, quartic form Lyapunov functional is utilized to stabilize the system with high amplified energy. Fourth-moment exponential stability conditions for the closed loop system are derived using It’s differential. Further, numerical examples are presented to show the applications of the theoretical results to physical systems. The effectiveness of the designed control function in the process of convergence of error vector are depicted in the form of error covariance matrices in the simulation.
期刊介绍：
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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