Almost equitable partitions and new necessary conditions for network controllability. (June 2017)

• Record Type: Journal Article
• Authors: Aguilar, Cesar O.; Gharesifard, Bahman
• Is Part Of: Automatica. Volume 80(2017)
• Page Start: 25
• Page End: 31
• Publication Date: 2017-06
• Subjects: Networked control systems -- Network controllability -- Equitable partitions; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2017.01.018
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In this paper, we consider the controllability problem for multi-agent networked control systems. The main results of the paper are new graph-theoretic necessary conditions for controllability involving almost equitable graph vertex partitions. We generalize the known results on the role of graph symmetries and uncontrollability to weighted digraphs with multiple-leaders and we also consider the broadcasted control scenario. Our results show that the internal structure of communities in a graph can induce obstructions to controllability that cannot be characterized by symmetry arguments alone and that in some cases depend on the number-theoretic properties of the communities. We show via examples that our results can be used to account for a large portion of uncontrollable inducing leader-selections that could not have otherwise been accounted for using symmetry results.