Emergent Behaviors of Cucker-Smale Flocks on Riemannian Manifolds

• 成果类型: Article
• 署名作者: Ha, Seung-Yeal; Kim, Doheon; Schloder, Franz Wilhelm
• 署名单位: Seoul National University (SNU); Seoul National University (SNU); Korea Institute for Advanced Study (KIAS); University of Milano-Bicocca
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3014096
• 发表日期: 2021
• 页码: 3020-3035
• 关键词: Manifolds; Mathematical model; ELECTRONIC MAIL; Heuristic algorithms; Couplings; Vehicle dynamics; Cucker-Smale model; flocking; geometric flocking; multiagent systems; Riemannian manifold

摘要

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 Poincare half-plane, and provide explicit reductions from the proposed general model to aforementioned manifolds via explicit formulas for the covariant derivative and parallel transport.