Constrained Containment Control for Multiagent Systems With Possible Empty Intersection of Position Constraints

The objective of this article is to study containment control problems for multiagent systems with position constraints and switching topologies. The first contribution is to find conditions under which all agents have the possibility to realize containment control in a distributed manner while the position of each agent is constrained to lie in a specific constraint set in the presence of possible conflicts of the position constraints and the requirement of the convergence into the convex hull of the leaders. The second contribution is to propose two nonlinear distributed algorithms for single-integrator and double-integrator multiagent systems and show that all agents finally converge to the convex hull of some given leaders even when the intersection of all constraint sets is empty. Finally, numerical examples are given to show the effectiveness of these algorithms.