Controllability of interconnected systems via switching networks with a leader

In this paper we study the property of controllability for a class of interconnected systems with a leader in switching networks. We obtain necessary and sufficient conditions for the interconnected systems using neighbor rules, to be controllable by one of them acting as a leader. Here, we take the control laws to be an attractive force, and we assume the topology of the control interconnections is variant, that is, each swarm individual (agent) updates is current state based on the current information from neighboring individuals and the leader. Results show that the interconnected systems can be completely controllable even though every subsystem cannot be controllable by selecting one of the as a leader and neighbor interaction rules. Moreover, the swarm can begin from the given initial configuration and reach a desired final configuration while satisfying certain conditions. The model and results of this paper present a novel method to investigate a class of swarms via switching systems and provide further insight into the effect of the interaction pattern on self-organized motion in a swarm system. Numerical simulations are also worked out to illustrate the analytical results.