Distributed L2 − L∞ containment control with nonconvex constraints for multi-agent systems

Abstract

This paper studies a distributed L2−L∞ containment control problem with or without considering nonconvex control input constraints. The main challenge is how to address nonconvex constraints while satisfying the L2−L∞ performance index function. A distributed algorithm is proposed using only the local information, and the containment control problem with nonconvex constraints and L2−L∞ performance can be solved. Based on the properties of the projection operator and convexity, the constrained L2−L∞ containment control problem can be solved under the undirected connected graphs. Finally, the effectiveness of the algorithm is verified by a numerical experiment.