一类具有时变延迟的分数阶非线性反应-扩散系统的稳定:事件触发边界控制方法

IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Ailiang Zhao , Junmin Li , Aili Fan
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引用次数: 0

摘要

基于混合事件触发机制(HETM),利用两种测量方法研究了具有时变延迟的分数阶非线性反应扩散系统(FNRDS)的边界稳定问题。首先,当系统状态可测量时,直接根据平均测量输出设计事件触发反馈控制器(ETFC)。其次,对于状态不可测量的情况,通过边界点测量信息构建基于观测器框架的事件触发反馈控制器。利用 Lyapunov 方法和 Wirtinger 不等式,分别以线性矩阵不等式(LMI)的形式给出了系统渐近稳定性的充分条件,其中使用了 Razumikhin 定理来处理时变延迟。同时,还证明了所设计的 HETM 可以排除芝诺行为。最后,数值模拟证明了所提控制方案的有效性和可行性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stabilization for a class of fractional-order nonlinear reaction–diffusion systems with time-varying delay: Event-triggered boundary control approach

Based on the hybrid event-triggered mechanism (HETM), the boundary stabilization issue for fractional-order nonlinear reaction–diffusion systems (FNRDSs) with time-varying delay is studied by using two kinds of measurements. First, when the system state is measurable, a event-triggered feedback controller (ETFC) is designed directly based on the average measured output. Secondly, for the case that the state is unmeasurable, an event-triggered feedback controller based on observer framework is constructed through the boundary point measurement information. Utilizing the Lyapunov method and Wirtinger’s inequality, sufficient conditions for the asymptotic stability of the system are given in the form of linear matrix inequalities (LMIs), respectively, in which the Razumikhin theorem is used to deal with time-varying delay. Meanwhile, it is proved that Zeno behavior can be excluded by the designed HETM. Finally, numerical simulations demonstrate the validity and feasibility of the proposed control scheme.

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来源期刊
Mathematics and Computers in Simulation
Mathematics and Computers in Simulation 数学-计算机:跨学科应用
CiteScore
8.90
自引率
4.30%
发文量
335
审稿时长
54 days
期刊介绍: The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.
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