New Results of Multi-Agent Controllability Under Equitable Partitions

Yanhong Lou,Jijun Qu,Zhijian Ji

doi:10.1109/access.2020.2988141

Yanhong Lou, Jijun Qu + Show 1 more

Open Access

https://doi.org/10.1109/access.2020.2988141

Copy DOI

Abstract

This paper studies the controllability of leader-follower multi-agent systems under fixed topology. The relationship between controllability and information communication topologies is characterized by taking advantage of equitable partitions. Firstly, for one non-trivial cell taking leaders role, a graph theory method is proposed to determine the multi-agent controllability. Secondly, the controllability of undirected graphs consisting of four nodes is analyzed in detail, and the limitation of the equitable partition in controllability analysis is pointed out for the first time. Thirdly, the results of four-node graphs are extended to general topologies, by which, we reveal the relationship between the ranks of controllability matrix of the quotient graph and original graph. Finally, the effect of non-trivial cells on the controllable subspace is analyzed from the viewpoint of controllability matrix and eigenvector.

Highlights

Multi-agent system (MAS) has been widely studied by many scholars in the field of control science
Proposition 2: The following two classes of topological structures cannot be judged for controllability by equitable partition methods: i) Under the maximal relaxed equitable partition, the leader is selected from the trivial cell, and the follower subgraph has only trivial equitable partitions
Example 4: Taking the equitable partition in Figure 16 as an example, when node 1 is selected as the leader, the controllability matrix and eigenvectors of the system are as follows

Summary

INTRODUCTION

Multi-agent system (MAS) has been widely studied by many scholars in the field of control science. Proposition 2: The following two classes of topological structures cannot be judged for controllability by equitable partition methods: i) Under the maximal relaxed equitable partition, the leader is selected from the trivial cell, and the follower subgraph has only trivial equitable partitions. Ii) Under the maximal relaxed equitable partition, non-trivial cells are selected to play leaders role, and there are no automorphism nodes in the follower subgraph. In both cases, it is necessary to exclude the following situations: one is that the leader is selected from the endpoint of the chain structure and the other is leader symmetric structure. Of topology, the controllability of the system cannot be judged by equitable partition methods when any non-trivial cell is selected to play the leader role. If the problems of matrix structure are solved, a more general conclusions can be obtained by using the equitable partition to judge the system controllability

CONTROLLABILITY ANALYSIS OF GENERAL TOPOLOGIES

CONTROLLABILITY OF SPECIAL GRAPHS

Findings

CONCLUSION