Consensus Tracking and Containment in Multiagent Networks With State Constraints

The ability of tracking is an important prerequisite for multiagent networks to perform collective activities. This article investigates the problem of containment for a weighted multiagent network with continuous-time agents under state constraints. The network is composed of uninformed and informed agents, where the latter receive external inputs. A new general class of distributed nonlinear controllers is designed for accomplishing both containment and consensus tracking, where the state of each agent is required to stay in its desired convex constraint set. We show that, by using matrix analysis, convex analysis, and Lyapunov theory, all agents eventually converge to the convex hull formed by the external inputs while they obey their constraints during the transience. No relationship is assumed between the convex hull and the intersection of all constraint sets. The consensus tracking problem with a single external input is also solved under this framework. As a generalization, we tackle the multiscaled constrained containment problem, where agents can specify their desired buffer zones by either zooming in or zooming out the convex hull. Numerical examples are provided to illustrate the theoretical results.