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

Abstract

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.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61375120, 61533001, 61374199).

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Correspondence to Long Wang.

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Lu, Z., Zhang, L. & Wang, L. Controllability analysis of multi-agent systems with switching topology over finite fields. Sci. China Inf. Sci. 62, 12201 (2019). https://doi.org/10.1007/s11432-017-9284-4

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Keywords

  • multi-agent systems
  • leader-follower structure
  • controllability
  • finite fields
  • switching topology