Containment control for second-order multiagent systems communicating over heterogeneous networks

The containment control is studied for the second-order multiagent systems over a heterogeneous network where the position and velocity interactions are different. We consider three cases that multiple leaders are stationary, moving at the same constant speed, and moving at the same time-varying speed, and develop different containment control algorithms for each case. In particular, for the former two cases, we first propose the containment algorithms based on the well-established ones for the homogeneous network, for which the position interaction topology is required to be undirected. Then, we extend the results to the general setting with the directed position and velocity interaction topologies by developing a novel algorithm. For the last case with time-varying velocities, we introduce two algorithms to address the containment control problem under, respectively, the directed and undirected interaction topologies. For most cases, sufficient conditions with regard to the interaction topologies are derived for guaranteeing the containment behavior and, thus, are easy to verify. Finally, six simulation examples are presented to illustrate the validity of the theoretical findings.