Variable gain intermittent stabilization and synchronization for delayed chaotic Lur’e systems

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-21 DOI:10.1016/j.cnsns.2024.108353

Yili Wang , Wu-Hua Chen , Xiaomei Lu

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Abstract

In this paper, a variable gain intermittent control strategy for stabilization and synchronization of chaotic Lur’e systems with time-varying delay is proposed. In contrast to the conventional constant gain intermittent control strategies, the proposed intermittent control strategy allows the control gain to vary with the operation duration of the intermittent controller. The construction of variable control gains is based on a partition scheme on the time-varying working intervals. In order to align with the structure of the variable intermittent control gain function, a pair of partition-dependent piecewise Lyapunov functions are introduced. Two distinct Razumikhin-type analysis techniques, one for the working intervals and the other for the resting intervals, are employed to derive novel criteria for intermittent stabilization and synchronization. The desired intermittent control/synchronization gain functions can be obtained by solving a convex minimization problem, which is capable of minimizing the control width under specified constraints on the gain norm. The numerical results demonstrate that, in comparison with the conventional constant gain strategies, the proposed variable gain intermittent control strategy is capable of efficiently reducing the intermittent control rate.

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延迟混沌鲁尔系统的可变增益间歇稳定和同步化

本文提出了一种可变增益间歇控制策略，用于稳定和同步具有时变延迟的混沌 Lur'e 系统。与传统的恒定增益间歇控制策略不同，本文提出的间歇控制策略允许控制增益随间歇控制器的运行时间而变化。可变控制增益的构建基于时变工作间隔的分区方案。为了与可变间歇控制增益函数的结构保持一致，引入了一对依赖于分区的片断 Lyapunov 函数。采用两种不同的拉祖米欣型分析技术，一种针对工作区间，另一种针对静止区间，从而推导出间歇稳定和同步的新标准。所需的间歇控制/同步增益函数可通过求解凸最小化问题获得，该问题能够在增益规范的特定约束条件下使控制宽度最小化。数值结果表明，与传统的恒定增益策略相比，所提出的可变增益间歇控制策略能够有效降低间歇控制率。

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.