Leaders in multi-agent controllability under consensus algorithm and tree topology

• Published in: Systems & control letters Vol. 61; no. 9; pp. 918 - 925
• Main Authors: Ji, Zhijian, Lin, Hai, Yu, Haisheng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.09.2012; Elsevier
• Subjects: Agents (artificial intelligence); Algorithms; Applied sciences; Artificial intelligence; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Control system analysis; Control theory. Systems; Controllability; Exact sciences and technology; Expert systems; Information retrieval. Graph; Leader–follower structure; Local interaction; Multi-agent system; Robot control; Robots; Software; Theoretical computing; Topology; Trees; Controllability; Leader–follower structure; Local interaction; Multi-agent system; Branching; Nearest neighbour; Tree(graph); Necessary and sufficient condition; Collective process; Distributed system; Topology; Consensus; Multiagent system; Heuristic method; Subgraph; Swarm intelligence; Leader―follower structure; Localization; Formation; Artificial intelligence; Reconfiguration
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2012.06.003

By controllability of multi-agent systems, we mean the property that all agents can be driven to arbitrary configurations only through regulating a few leaders externally, while the rest of the agents are subject to the nearest-neighbor-law. It is known that the controllability of multi-agent systems depends not only on the communication topologies among agents but also on the selection of leaders. The main objective of this paper aims to characterize the virtue that leaders should have from the perspective of algebraic and graphical conditions. We begin with a heuristic observation for tree graph. To gain more insights, necessary and sufficient conditions are then proposed in terms of downer branch and subgraphs, respectively. In particular, it is shown for path topologies that controllability completely depends on the leaders’ location. The obtained results may help us to pave the way towards a new method of formation and reconfiguration control in swarming robots.