TY - JOUR
T1 - The Domain of Attraction of the Desired Path in Vector-Field-Guided Path Following
AU - Yao, Weijia
AU - Lin, Bohuan
AU - Anderson, Brian D.O.
AU - Cao, Ming
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023/11
Y1 - 2023/11
N2 - 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×S1 , and not just homotopy equivalent to S1.
AB - 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×S1 , and not just homotopy equivalent to S1.
KW - Domain of attraction, nonlinear systems
UR - http://www.scopus.com/inward/record.url?scp=85147313058&partnerID=8YFLogxK
U2 - 10.1109/TAC.2023.3239431
DO - 10.1109/TAC.2023.3239431
M3 - Article
SN - 0018-9286
VL - 68
SP - 6812
EP - 6819
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 11
ER -