SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 724-751, February 2024.
Abstract. This paper studies a leader-following rendezvous problem for the generalized Cucker–Smale model, a double-integrator multiagent system, on some Riemannian manifolds. By using intrinsic properties of the covariant derivative, logarithmic map, and parallel transport on the Riemannian manifolds, we design a feedback control law and prove that this feedback control law enables all followers to track the trajectory of the moving leader when the Riemannian manifold is compact or flat. As concrete examples, we consider the leader-following rendezvous problem on the unit sphere, in Euclidean space, on the unit circle, and infinite cylinder and present the corresponding feedback control laws. Meanwhile, numerical examples are given for the aforementioned Riemannian manifolds to illustrate and verify the theoretical results.

中文翻译：

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黎曼流形上广义Cucker-Smale模型的引导-跟随交会控制

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 724-751 页，2024 年 2 月。
摘要。本文研究了广义 Cucker-Smale 模型（一种双积分多智能体系统）在某些黎曼流形上的领导者跟随交会问题。利用黎曼流形上的协变导数、对数映射和并行传输的内在性质，设计了反馈控制律，并证明了当黎曼流形紧致时，该反馈控制律使所有跟随者能够跟踪移动引导者的轨迹或平坦。作为具体例子，我们考虑了单位球面、欧氏空间、单位圆和无限圆柱上的引导跟随交会问题，并给出了相应的反馈控制律。同时对上述黎曼流形给出数值算例来说明和验证理论结果。