This paper studies the cooperative set aggregation problem for second-order multiagent systems by utilizing the approximate projection algorithm. First, an aggregation law that uses the approximate projection is proposed, where the feasible set of the approximate projection points is established based on an Euclidean distance with respect to the targeted set and a deviated angle with respect to the exact projection point. Under the proposed law, the position vectors of all the agents are shown to reach an agreement in the intersection of their individual targeted sets and the velocity vector of each agent is shown to converge to zero. Then, a time-dependent performance bound is set for the norm of the weighted error of the relative positions among neighboring agents and the absolute velocity of the agent, and a performance-guaranteed aggregation controller is designed to guarantee the prescribed transient performance. During the process of aggregation, the norm of the weighted error is shown to not exceed the performance bound. The convergence conditions of the proposed algorithms with respect to the control strength and the terms induced by the approximate projection are obtained by using the techniques of convex analysis and Lyapunov stability. Simulations are provided to validate the theoretical results.

中文翻译：

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二阶多智能体系统的协作集聚合：近似投影和规定性能


本文利用近似投影算法研究二阶多智能体系统的协作集聚合问题。首先，提出了一种使用近似投影的聚合律，其中基于相对于目标集合的欧氏距离和相对于精确投影点的偏离角度来建立近似投影点的可行集合。根据所提出的定律，所有智能体的位置向量在其各自的目标集的交集中都达到了一致，并且每个智能体的速度向量都收敛到零。然后，为相邻智能体之间相对位置的加权误差范数和智能体的绝对速度设置一个与时间相关的性能界限，并设计一个性能保证的聚合控制器来保证规定的瞬态性能。在聚合过程中，加权误差的范数显示不超过性能界限。利用凸分析和李亚普诺夫稳定性技术获得了所提出算法在控制强度和近似投影导出项方面的收敛条件。提供模拟来验证理论结果。