{"title":"Leader-Following Formation Control for Discrete-Time Fractional Stochastic Multi-Agent Systems by Event-Triggered Strategy","authors":"Jiawei Wu, Yongguang Yu, Guojian Ren","doi":"10.3390/fractalfract8050246","DOIUrl":null,"url":null,"abstract":"Fractional differential equations, which are non-local and can better describe memory and genetic properties, are widely used to describe various physical, chemical, and biological phenomena. Therefore, the multi-agent systems based on discrete-time fractional stochastic models are established. First, some followers are selected for pinning control. In order to save resources and energy, an event-triggered based control mechanism is proposed. Second, under this control mechanism, sufficient conditions on the interaction graph and the fractional derivative order such that formation control can be achieved are given. Additionally, influenced by noise, the multi-agent system completes formation control in the mean square. In addition to that, these results are equally applicable to the discrete-time fractional formation problem without noise. Finally, the example of numerical simulation is given to prove the correctness of the results.","PeriodicalId":12435,"journal":{"name":"Fractal and Fractional","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractal and Fractional","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3390/fractalfract8050246","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Fractional differential equations, which are non-local and can better describe memory and genetic properties, are widely used to describe various physical, chemical, and biological phenomena. Therefore, the multi-agent systems based on discrete-time fractional stochastic models are established. First, some followers are selected for pinning control. In order to save resources and energy, an event-triggered based control mechanism is proposed. Second, under this control mechanism, sufficient conditions on the interaction graph and the fractional derivative order such that formation control can be achieved are given. Additionally, influenced by noise, the multi-agent system completes formation control in the mean square. In addition to that, these results are equally applicable to the discrete-time fractional formation problem without noise. Finally, the example of numerical simulation is given to prove the correctness of the results.
期刊介绍:
Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.