Containment Control with Different Constraints

This article addresses a containment control problem for discrete-time multiagent systems when position, velocity, and input constraints coexist. A nonlinear distributed containment control algorithm is presented. The main difficulty is how to decouple the nonlinearities caused by the three kinds of constraints. To prove the convergence of the containment control problem, the distances from the followers to the convex hull spanned by the leaders are analyzed by removing the errors caused by the projection operators and the stochasticities of the equivalent system matrices are explored to show nonincreasing property of the maximum distance. It is shown that containment control can be achieved as long as the convex hull is contained in each position constraint set. Numerical simulations are given to illustrate the obtained theoretical results.