Controllability analysis of multi-agent systems with switching topology over finite fields

In this paper, we investigate the controllability problem of multi-agent systems with switching topology over finite fields. The multi-agent system is defined over finite fields, where agents process only values from a finite alphabet. Under leader-follower structure, one agent is selected as a leader for each subsystem. First, we prove that a multi-agent system with switching topology is controllable over a finite field if the graph of the subsystem is a spanning forest, and the size of the field is sufficiently large. Second, we show that, by appropriately selecting leaders, the multi-agent system with switching topology can be controllable over a finite field even if each of its subsystems is not controllable. Specifically, we show that the number of leaders for ensuring controllability of the switched multi-agent system is less than the minimum number of leaders for ensuring the controllability of all subsystems. Finally, it is proved that the multi-agent system is controllable over a finite field if the union of the graphs is a directed path graph or a star graph.