ABSTRACT
This chapter provides the distributed containment control problem for multi-agent systems with general linear dynamics. Distributed dynamic containment controllers based on the relative outputs of neighboring agents are proposed for both the continuous-time and discrete-time cases. In the continuous-time case, a multistep algorithm is presented to construct a dynamic containment controller, under which the states of the followers will asymptotically converge to the convex hull formed by those of the leaders, if for each follower there exists at least one leader that has a directed path to that follower. In the discrete-time case, in light of the modified algebraic Riccati equation, an algorithm is given to design a dynamic containment controller that solves the containment control problem. The containment control problem for the general case where the leaders have nonzero, bounded, and time-varying control inputs.
