{"title":"基于障碍函数的高阶非线性系统自适应轨迹跟踪控制与碰撞规避","authors":"","doi":"10.1016/j.amc.2024.129004","DOIUrl":null,"url":null,"abstract":"<div><p>This paper considers the problem of trajectory tracking and collision avoidance for a class of high-order nonlinear strict feedback systems with unknown nonlinearities. The main issue is how to ensure collision avoidance and tracking performance simultaneously in the presence of unknown nonlinear functions. To address the issue, an integral-multiplicative barrier Lyapunov function (BLF) is integrated into the backstepping procedure to remove the dynamic mismatching issue of the existing SUM-type BLF. It has been proven that the proposed adaptive approach ensures both collision avoidance and tracking performance of high-order nonlinear systems in multi-obstacle environments, and all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Simulation results confirm the effectiveness of the proposed method.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S009630032400465X/pdfft?md5=e79b3cb137499d266b1f6277a6d046cf&pid=1-s2.0-S009630032400465X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Barrier-function based adaptive trajectory tracking control for high-order nonlinear systems with collision avoidance\",\"authors\":\"\",\"doi\":\"10.1016/j.amc.2024.129004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper considers the problem of trajectory tracking and collision avoidance for a class of high-order nonlinear strict feedback systems with unknown nonlinearities. The main issue is how to ensure collision avoidance and tracking performance simultaneously in the presence of unknown nonlinear functions. To address the issue, an integral-multiplicative barrier Lyapunov function (BLF) is integrated into the backstepping procedure to remove the dynamic mismatching issue of the existing SUM-type BLF. It has been proven that the proposed adaptive approach ensures both collision avoidance and tracking performance of high-order nonlinear systems in multi-obstacle environments, and all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Simulation results confirm the effectiveness of the proposed method.</p></div>\",\"PeriodicalId\":55496,\"journal\":{\"name\":\"Applied Mathematics and Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.5000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S009630032400465X/pdfft?md5=e79b3cb137499d266b1f6277a6d046cf&pid=1-s2.0-S009630032400465X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S009630032400465X\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S009630032400465X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
本文探讨了一类具有未知非线性的高阶非线性严格反馈系统的轨迹跟踪和避免碰撞问题。主要问题是如何在存在未知非线性函数的情况下同时确保避免碰撞和跟踪性能。为了解决这个问题,我们将积分-乘法障碍李亚普诺夫函数(BLF)集成到反步进程序中,以消除现有 SUM 型 BLF 的动态不匹配问题。实验证明,所提出的自适应方法能确保高阶非线性系统在多障碍物环境下的防碰撞和跟踪性能,并且闭环系统中的所有信号都是均匀终极有界(UUB)的。仿真结果证实了所提方法的有效性。
Barrier-function based adaptive trajectory tracking control for high-order nonlinear systems with collision avoidance
This paper considers the problem of trajectory tracking and collision avoidance for a class of high-order nonlinear strict feedback systems with unknown nonlinearities. The main issue is how to ensure collision avoidance and tracking performance simultaneously in the presence of unknown nonlinear functions. To address the issue, an integral-multiplicative barrier Lyapunov function (BLF) is integrated into the backstepping procedure to remove the dynamic mismatching issue of the existing SUM-type BLF. It has been proven that the proposed adaptive approach ensures both collision avoidance and tracking performance of high-order nonlinear systems in multi-obstacle environments, and all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Simulation results confirm the effectiveness of the proposed method.
期刊介绍:
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.