Emergent behaviors of Cucker-Smale flocks on a Riemannian manifolds
- Title
- Emergent behaviors of Cucker-Smale flocks on a Riemannian manifolds
- Author
- 김도헌
- Keywords
- Cucker–Smale model; flocking; geometric flocking; multiagent systems; Riemannian manifold
- Issue Date
- 2021-07
- Publisher
- IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
- Citation
- IEEE TRANSACTIONS ON AUTOMATIC CONTROL; JUL 2021, 66 7, p3020-p3035, 16p.
- Abstract
- In this article, we present a new Cucker–Smale
model on smooth Riemannian manifolds using the concepts of covariant derivative and parallel transport, and we
also study its emergent dynamics under an a priori assumption on the energy functional. For Euclidean space, our
proposed model coincides with the original Cucker–Smale
model. As concrete examples, we consider three Riemannian manifolds: the unit 2-sphere, the unit circle, and the
Poincaré half-plane, and provide explicit reductions from
the proposed general model to aforementioned manifolds
via explicit formulas for the covariant derivative and parallel
transport.
- URI
- https://ieeexplore.ieee.org/document/9157958https://repository.hanyang.ac.kr/handle/20.500.11754/172605
- ISSN
- 00189286; 15582523
- DOI
- 10.1109/TAC.2020.3014096
- Appears in Collections:
- COLLEGE OF SCIENCE AND CONVERGENCE TECHNOLOGY[E](과학기술융합대학) > APPLIED MATHEMATICS(응용수학과) > Articles
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