Stabilization of coupled nonlinear systems with Lévy noise and time-varying delays

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-26 DOI:10.1016/j.cnsns.2025.108878

Wanying Guo , Yao Feng , Wenxue Li

引用次数: 0

Abstract

In this paper, the stabilization problem of coupled nonlinear systems with Lévy noise and time-varying delays is discussed via pinning control. It is the first time for stochastic nonlinear strict-feedback systems to consider couplings, time-varying delays, and Lévy noise simultaneously. Furthermore, different from other common control strategies, the pinning control can effectually save the control cost because it can selectively control a fraction of nodes to reach stabilization. Additionally, the design of actual controllers is accomplished by backstepping method and designing virtual controllers. Subsequently, by integrating the Lyapunov method with graph theory, we construct a global Lyapunov function and establish a stabilization criterion. Moreover, the stabilization problem for a class of coupled robotic arm systems is studied as practical applications. Finally, numerical simulations are presented to demonstrate the feasibility of the theoretical results.

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具有lsamvy噪声和时变时滞的耦合非线性系统的镇定

本文讨论了一类具有lsamvy噪声和时变时滞的耦合非线性系统的钉住控制镇定问题。这是随机非线性严格反馈系统首次同时考虑耦合、时变时滞和lsamvy噪声。此外，与其他常用的控制策略不同，钉住控制可以选择性地控制一小部分节点以达到稳定，从而有效地节省了控制成本。通过反推法和虚拟控制器的设计，完成了实际控制器的设计。然后，将Lyapunov方法与图论相结合，构造了一个全局Lyapunov函数，并建立了一个稳定判据。在此基础上，结合实际应用研究了一类耦合机械臂系统的镇定问题。最后通过数值模拟验证了理论结果的可行性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.