Global Coordinated Stabilization of Multiple Simple Mechanical Control Systems on a Class of Lie Groups

• 成果类型: Article
• 署名作者: Tong, Xin; Ding, Qingpeng; Cheng, Shing Shin
• 署名单位: Nanjing University; Chinese University of Hong Kong; Chinese University of Hong Kong; Chinese University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3486648
• 发表日期: 2025
• 页码: 2043-2050
• 关键词: Lie groups; asymptotic stability; vectors; State feedback; Multi-agent systems; MANIFOLDS; Transmission line matrix methods; tail; Synchronization; Image edge detection; Cooperative control; hybrid systems; stability of nonlinear systems; synergistic hybrid feedback

摘要

This article investigates the problem of global coordinated stabilization for a multiagent system, which consists of a general class of mechanical systems that evolve on compact connected Lie groups. First, a distributed synergistic hybrid controller is synthesized by leveraging a coadjoint incidence matrix to assign to neighboring agents a hybrid feedback that is based on their relative position. It leads to robust and global asymptotic stability in tree networks. Second, the existence of synergistic potential functions (SPFs)-the key ingredient for deriving the hybrid feedback-is established on compact Lie groups. Moreover, a direct extension shows that there exists an SPF on the noncompact special Euclidean group SE(n). In contrast with some existing results, the proposed controller removes the invariance condition on the hybrid feedback, and the existence of the SPF ensures that our controller is applicable to many Lie groups of practical interests. Finally, a worked example of multiple planar rigid-body systems on SE(2) is used to illustrate our approach.