Distributed Prescribed-Time Interval Bipartite Consensus of Multi-Agent Systems on Directed Graphs: Theory and Experiment

• Published in: IEEE transactions on network science and engineering Vol. 8; no. 1; pp. 613 - 624
• Main Authors: Gong, Xin, Cui, Yukang, Shen, Jun, Shu, Zhan, Huang, Tingwen
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.01.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bipartite consensus; Directed graphs; Eigenvalues and eigenfunctions; Graph theory; Graphs; Helicopters; Laplace equations; Liapunov functions; Multi-agent systems; Multiagent systems; prescribed-time consensus; Protocols; Symmetric matrices; System effectiveness; Topology
• ISSN: 2327-4697; 2334-329X
• DOI: 10.1109/TNSE.2020.3047232

This work deals with the analysis and protocol design problems of the prescribed-time interval bipartite consensus of multi-agent systems on signed and directed graphs. A new distributed protocol with hybrid constant and time-varying feedbacks of local signed error is proposed, whose consensus time period is independent of the specific topology among agents and initial states of all agents. By introducing a series of well-structured Lyapunov functions, the technical difficulties arising from the asymmetrical Laplacian matrices of directed graphs are circumvented. The effectiveness of this prescribed-time protocol for multi-agent systems on signed digraphs with a spanning tree is proven both on structurally balanced digraphs and structurally unbalanced ones with a positive root subgraph. An illustrative simulation example and a prescribed-time bipartite formation experiment on a swarm of nano-quadcopters are implemented to show the validity and practicability of these proposed protocols.