非线性随机抛物型分布参数系统的均方有限定时稳定性

IF 3.8 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-02-24 DOI:10.1016/j.cnsns.2025.108688

Xisheng Dai , Yang Xu , Feiqi Deng

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引用次数: 0

摘要

研究了一类非线性随机抛物型分布参数系统的均方有限时间稳定性和均方规定时间稳定性。引入内部动态变量，设计动态周期事件触发机制（DPETM）。此外，结合两种不同的调整函数，提出了一种新的定时DPETM，以降低控制器的更新频率。在设计分布式控制器的基础上，分别以线性矩阵不等式（lmi）的形式给出了闭环系统的msft和MSPTS的充分条件。这里使用了Lyapunov-Krasovskii泛函方法、积分不等式和洛必达法则。最后，通过两个数值算例验证了所提出的有限时间和规定时间控制算法的有效性。

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Mean-square finite and prescribed-time stability for nonlinear stochastic parabolic distributed parameter systems

In this paper, the mean-square finite-time stability (MSFTS) and mean-square prescribed-time stability (MSPTS) of a class of nonlinear stochastic parabolic distributed parameter systems are studied. An internal dynamic variable is introduced to design dynamic periodic event-triggered mechanism (DPETM) for FTS. Moreover, a new prescribed-time DPETM is proposed by combining two different adjustment functions to reduce the update frequency of the controller. Based on designing distributed controllers, the sufficient conditions for the closed-loop system’s MSFTS and MSPTS are provided in the form of linear matrix inequalities (LMIs), respectively. Here, the Lyapunov–Krasovskii functional method, integral inequality, and L’Hospital’s rule are used. Finally, two numerical examples verify the effectiveness of the proposed finite-time and prescribed-time control algorithms.

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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.