The Domain of Attraction of the Desired Path in Vector-Field-Guided Path Following

• 成果类型: Article
• 署名作者: Yao, Weijia; Lin, Bohuan; Anderson, Brian D. O.; Cao, Ming
• 署名单位: Hunan University; University of Groningen; University of Groningen; Australian National University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3239431
• 发表日期: 2023
• 页码: 6812-6819
• 关键词: Domain of attraction; nonlinear systems.

摘要

In the vector-field-guided path-following problem, a sufficiently smooth vector field is designed such that its integral curves converge to and move along a 1-D geometric desired path. The existence of singular points where the vector field vanishes creates a topological obstruction to global convergence to the desired path and some associated topological analysis has been conducted in our previous work. In this article, we further show that the domain of attraction of the desired path, which is a compact asymptotically stable 1-D embedded submanifold of an n-dimensional ambient manifold M, is homeomorphic to Rn-1 x S-1, and not just homotopy equivalent to S-1.