Containment control of networked Lagrange systems with group dispersion and cohesion behaviors

In this paper, distributed containment control with group dispersion and cohesion behaviors are discussed for a group of Lagrange systems. Both the cases of constant leaders´ generalized coordinate derivatives and time-varying leaders´ generalized coordinate derivatives are considered. The proposed control algorithms are shown to obtain velocity matching, connectivity maintenance and collision avoidance. In addition, the sum of the steady-state distances between followers and the convex hull formed by the leaders is shown to be bounded and this bound is explicitly given.