Position-constrained containment for second-order discrete-time multi-agent systems

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.