Event-triggered impulsive control for nonlinear stochastic delayed systems and complex networks

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-09-12 DOI:10.1016/j.cnsns.2024.108305

Junyan Xu , Yang Liu , Jianlong Qiu , Jianquan Lu

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Abstract

In this paper, we probe the $p$ th moment exponential stability ( $p -$ ES) of stochastic delayed systems subject to event-triggered delayed impulsive control (ETDIC), where the impulsive intensities are assumed to be positive random variables. Based on event-triggered mechanism (ETM) in the sense of expectation, some new sufficient conditions are developed to ensure the stability of the addressed system with Zeno-free behavior. The Lyapunov–Razumikhin method is adopted to handle the time-varying delay in continuous dynamics, and the concept of average random impulsive estimation (ARIE) is introduced to reduce the design requirements of the controller. Especially, the proposed ETDIC strategy not only generates the impulse time sequence according to the predesigned ETM, but also removes the limitations on the size of time delays. Furthermore, the ETM serves as a solution for synchronization problems in complex neural networks. Finally, two examples are given to illustrate the effectiveness of our conclusions.

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非线性随机延迟系统和复杂网络的事件触发脉冲控制

本文探讨了受事件触发延迟脉冲控制（ETDIC）影响的随机延迟系统的 pth 矩指数稳定性（p-ES），其中假设脉冲强度为正随机变量。基于期望意义上的事件触发机制（ETM），提出了一些新的充分条件，以确保所处理的系统具有无 Zeno 行为的稳定性。采用 Lyapunov-Razumikhin 方法处理连续动力学中的时变延迟，并引入平均随机脉冲估计（ARIE）的概念以降低控制器的设计要求。特别是，所提出的 ETDIC 策略不仅能根据预先设计的 ETM 生成脉冲时间序列，还能消除对时间延迟大小的限制。此外，ETM 还是复杂神经网络中同步问题的一种解决方案。最后，我们举了两个例子来说明我们结论的有效性。

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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.