{"title":"多目标包围控制问题的时变几何中心的无喋喋不休和有限时间估计","authors":"Liang Zhang , Jun Song , Shuping He","doi":"10.1016/j.jfranklin.2024.107394","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates the finite-time estimation of the time-varying Geometrical Center of Targets (GCT) in Multi-Target Enclosing Control Problem (MTECP). Existing estimators exhibit a chattering phenomenon that is harmful to the mechanical components of the deployed robots when forming the enclosing formation. We thereby propose two chattering-free finite-time estimators, employing a fully distributed approach demanding only the local observation and neighboring communication. The first fractional-order estimator is formulated by replacing the discontinuous term in the existing finite-time estimator by a fractional-order term, which remains smooth when the consensus error approaches zero. Theoretical results show that the estimation error can be stabilized into a bounded region adjustable by tuning the parameters. Then, another novel estimator with double integral architecture is designed to further eliminate the bounded estimation error in the first-order estimator i.e. can achieve exact tracking of the GCT in finite-time. Its continuity of estimation arises from the integration of a discontinuous unit-vector term and three more internal states are introduced to realize the double integral architecture. Finally, simulation and comparison results validate the correctness and smoothness of the proposed estimators.</div></div>","PeriodicalId":17283,"journal":{"name":"Journal of The Franklin Institute-engineering and Applied Mathematics","volume":"362 1","pages":"Article 107394"},"PeriodicalIF":3.7000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chattering-free and finite-time estimation of the time-varying geometrical center for the multi-targets enclosing control problem\",\"authors\":\"Liang Zhang , Jun Song , Shuping He\",\"doi\":\"10.1016/j.jfranklin.2024.107394\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper investigates the finite-time estimation of the time-varying Geometrical Center of Targets (GCT) in Multi-Target Enclosing Control Problem (MTECP). Existing estimators exhibit a chattering phenomenon that is harmful to the mechanical components of the deployed robots when forming the enclosing formation. We thereby propose two chattering-free finite-time estimators, employing a fully distributed approach demanding only the local observation and neighboring communication. The first fractional-order estimator is formulated by replacing the discontinuous term in the existing finite-time estimator by a fractional-order term, which remains smooth when the consensus error approaches zero. Theoretical results show that the estimation error can be stabilized into a bounded region adjustable by tuning the parameters. Then, another novel estimator with double integral architecture is designed to further eliminate the bounded estimation error in the first-order estimator i.e. can achieve exact tracking of the GCT in finite-time. Its continuity of estimation arises from the integration of a discontinuous unit-vector term and three more internal states are introduced to realize the double integral architecture. Finally, simulation and comparison results validate the correctness and smoothness of the proposed estimators.</div></div>\",\"PeriodicalId\":17283,\"journal\":{\"name\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"volume\":\"362 1\",\"pages\":\"Article 107394\"},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of The Franklin Institute-engineering and Applied Mathematics\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0016003224008159\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of The Franklin Institute-engineering and Applied Mathematics","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0016003224008159","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Chattering-free and finite-time estimation of the time-varying geometrical center for the multi-targets enclosing control problem
This paper investigates the finite-time estimation of the time-varying Geometrical Center of Targets (GCT) in Multi-Target Enclosing Control Problem (MTECP). Existing estimators exhibit a chattering phenomenon that is harmful to the mechanical components of the deployed robots when forming the enclosing formation. We thereby propose two chattering-free finite-time estimators, employing a fully distributed approach demanding only the local observation and neighboring communication. The first fractional-order estimator is formulated by replacing the discontinuous term in the existing finite-time estimator by a fractional-order term, which remains smooth when the consensus error approaches zero. Theoretical results show that the estimation error can be stabilized into a bounded region adjustable by tuning the parameters. Then, another novel estimator with double integral architecture is designed to further eliminate the bounded estimation error in the first-order estimator i.e. can achieve exact tracking of the GCT in finite-time. Its continuity of estimation arises from the integration of a discontinuous unit-vector term and three more internal states are introduced to realize the double integral architecture. Finally, simulation and comparison results validate the correctness and smoothness of the proposed estimators.
期刊介绍:
The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.