Abstract In this paper, we study a containment control problem for second-order multi-agent systems in the presence of convex position constraints and switching graphs. A distributed algorithm with a nonlinear projection operator is proposed to guarantee that each agent eventually converges into the convex hull spanned by some given multiple static points, while the position of each agent is kept lying in a given closed set. It is proved that all agents ultimately converge into the convex hull while each agent remains in its constraint set as long as there exists a directed path from the static points to the agents in the union of the graphs in each bounded time interval. Finally, a numerical example is given to illustrate the obtained theoretical results.

中文翻译：

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二阶离散时间多智能体系统的位置约束包含

摘要 在本文中，我们研究了存在凸位置约束和切换图的二阶多智能体系统的包含控制问题。提出了一种具有非线性投影算子的分布式算法，以保证每个代理最终收敛到由一些给定的多个静态点跨越的凸包，而每个代理的位置保持在给定的闭集中。证明只要在每个有界时间间隔内存在从静态点到图的联合中的代理的有向路径，所有代理最终都会收敛到凸包中，而每个代理仍保留在其约束集中。最后，给出一个数值例子来说明所得到的理论结果。