This paper addresses the problem of achieving finite‐time fault‐tolerant consensus control for a class of non‐linear fractional‐order multi‐agent systems (NFO‐MAS) using finite‐time fault detection and estimation, as well as a finite‐time state observer. To achieve this, a specific lemma is utilized to rewrite the high‐order model of NFO‐MAS as a lower‐order NFO unique system. By employing new identification rules and introducing a fault estimation method, both the state variables and faults of the agents are estimated within a finite time. Subsequently, a finite‐time sliding mode control law is designed based on the estimated fault and the state variables obtained from the proposed finite‐time observer to achieve consensus within a finite time for the fractional‐order non‐linear MAS. The stability of the fault estimation, state observer, and consensus controller is proven using the finite‐time Lyapunov theory. The effectiveness of the proposed approach is demonstrated through numerical simulations.
本文探讨了如何利用有限时间故障检测和估计以及有限时间状态观测器，为一类非线性分数阶多代理系统（NFO-MAS）实现有限时间容错共识控制的问题。为实现这一目标，利用一个特定的阶式将 NFO-MAS 的高阶模型重写为一个低阶 NFO 唯一系统。通过采用新的识别规则和引入故障估计方法，可以在有限时间内对代理的状态变量和故障进行估计。随后，根据故障估计和有限时间观测器得到的状态变量设计有限时间滑模控制法则，从而在有限时间内实现分数阶非线性 MAS 的共识。利用有限时间 Lyapunov 理论证明了故障估计、状态观测器和共识控制器的稳定性。通过数值模拟证明了所提方法的有效性。
{"title":"Hybrid finite‐time fault‐tolerant consensus control of non‐linear fractional order multi‐agent systems based on fault detection and estimation","authors":"Mahmood Nazifi, M. Pourgholi","doi":"10.1049/cth2.12627","DOIUrl":"https://doi.org/10.1049/cth2.12627","url":null,"abstract":"This paper addresses the problem of achieving finite‐time fault‐tolerant consensus control for a class of non‐linear fractional‐order multi‐agent systems (NFO‐MAS) using finite‐time fault detection and estimation, as well as a finite‐time state observer. To achieve this, a specific lemma is utilized to rewrite the high‐order model of NFO‐MAS as a lower‐order NFO unique system. By employing new identification rules and introducing a fault estimation method, both the state variables and faults of the agents are estimated within a finite time. Subsequently, a finite‐time sliding mode control law is designed based on the estimated fault and the state variables obtained from the proposed finite‐time observer to achieve consensus within a finite time for the fractional‐order non‐linear MAS. The stability of the fault estimation, state observer, and consensus controller is proven using the finite‐time Lyapunov theory. The effectiveness of the proposed approach is demonstrated through numerical simulations.","PeriodicalId":502998,"journal":{"name":"IET Control Theory & Applications","volume":"118 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139836706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hongjia Sha, Ju H. Park, Jun Chen, Mingbo Zhu, Chengjie Nan
This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods.
{"title":"Stability analysis of discrete‐time systems with a time‐varying delay via improved methods","authors":"Hongjia Sha, Ju H. Park, Jun Chen, Mingbo Zhu, Chengjie Nan","doi":"10.1049/cth2.12632","DOIUrl":"https://doi.org/10.1049/cth2.12632","url":null,"abstract":"This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods.","PeriodicalId":502998,"journal":{"name":"IET Control Theory & Applications","volume":"65 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139851913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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