Containment control of general linear multi-agent systems with multiple dynamic leaders: A fast sliding mode based approach

In this paper, distributed containment control problems of general linear multi-agent systems are investigated. The objective is to make the followers in a multi-agent network converge to the convex hull spanned by some leaders whose control inputs are nonzero and not available to any followers. Sliding mode surfaces are defined for the cases of reduced order and non-reduced order, respectively. For each case, fast sliding mode controllers are designed. It is shown that all the error trajectories exponentially reach the sliding mode surfaces in a finite time if for each follower, there exists at least one of the leaders who has a directed path to the follower, and the leaders' control inputs are bounded. The control Lyapunov function for exponential finite time stability, motivated by the fast terminal sliding mode control, is used to prove reachability of the sliding mode surfaces. Simulation examples are given to illustrate the theoretical results.