Average Consensus on Arbitrary Strongly Connected Digraphs With Time-Varying Topologies

• Published in: IEEE transactions on automatic control Vol. 59; no. 4; pp. 1066 - 1071
• Main Authors: Kai Cai, Ishii, Hideaki
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-04-2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Automatic control; Balancing; Convergence; Distributed consensus; Graph theory; Heuristic algorithms; jointly strongly connected digraphs; Joints; multi-agent systems; Multiagent systems; Network topology; Networks; Reagents; surplus-based averaging; Switches; time-varying network topologies; Topology
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2014.2305952

We have recently proposed a "surplus-based" algorithm which solves the multi-agent average consensus problem on general strongly connected and static digraphs. The essence of that algorithm is to employ an additional variable to keep track of the state changes of each agent, thereby achieving averaging even though the state sum is not preserved. In this note, we extend this approach to the more interesting and challenging case of time-varying topologies: An extended surplus-based averaging algorithm is designed, under which a necessary and sufficient graphical condition is derived that guarantees state averaging. The derived condition requires only that the digraphs be arbitrary strongly connected in a joint sense, and does not impose "balanced" or "symmetric" properties on the network topology, which is therefore more general than those previously reported in the literature.