Containment control with input and velocity constraints

Abstract

In this paper, containment control for double-integrator discrete-time multi-agent systems is investigated with switching graphs, nonconvex input constraints and nonconvex velocity constraints. In order to eliminate the nonlinearities caused by the nonconvex input and velocity constraints, we first introduce two time-varying scaling factors to transform the original constrained system into an unconstrained time-varying linear one. By proposing an inductive method based on the lower bounds of the scaling factors, we decouple the relevance of the two kinds of constraints and transform the obtained time-varying system into a new equivalent system. It is shown that all agents converge into the convex hull of the leaders even when switching graphs, nonconvex control input constraints and nonconvex velocity constraints coexist, as long as there exists at least one directed path from one of the leaders to each agent in the union of the communication graphs. Finally, a simulation example is given to illustrate the obtained theoretical results.