Improved multi-agent controllability processing technique based on equitable partition

In this paper, we study the controllability of multi-agent systems by equitable partition and automorphism. For the case that cells are incompletely connected outside but completely connected inside, a necessary condition for controllability is given from the perspective of the rank of connection matrix. For the case of multiple cells being completely connected outside and incompletely connected inside, in terms of the eigenvalues and eigenvectors of L and L & pi;, several sufficient and necessary conditions for controllability are presented. Once the quotient graph is controllable under single input or all nodes in nontrivial cells are leaders, the lower bound of controllable subspace is determined. Finally, we give the gap between the necessary condition and the sufficient condition for controllability from the aspect of equitable partition. One highlight of the results in this paper is that we show sufficient conditions to judge controllability by equitable partition and automorphism, which, for specific cases, provides one method that how to break through the defect that equitable partition can only obtain necessary conditions.& COPY; 2023 ISA. Published by Elsevier Ltd. All rights reserved.

Automated summary

In this paper, the controllability of multi-agent systems is studied using equitable partition and automorphism. Necessary conditions for controllability are presented from the perspective of the rank of connection matrix when cells are incompletely connected outside but completely connected inside. Sufficient and necessary conditions for controllability are given based on the eigenvalues and eigenvectors of L and L & pi; when multiple cells are completely connected outside and incompletely connected inside. The paper also explores the gap between the necessary condition and the sufficient condition for controllability from the aspect of equitable partition.