Adaptive Event-Triggered Consensus of Multiagent Systems on Directed Graphs

• Published in: IEEE transactions on automatic control Vol. 66; no. 4; pp. 1670 - 1685
• Main Authors: Li, Xianwei, Sun, Zhiyong, Tang, Yang, Karimi, Hamid Reza
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive control; consensus; Control Engineering; Control systems; Directed graphs; Eigenvalues and eigenfunctions; Electrical Engineering, Electronic Engineering, Information Engineering; Elektroteknik och elektronik; Engineering and Technology; event-triggering control; Graph theory; Graphs; Laplace equations; Linear systems; Multi-agent systems; Multiagent systems; multiagent systems (MASs); Protocols; Reglerteknik; Teknik
• ISSN: 0018-9286; 2334-3303; 1558-2523
• DOI: 10.1109/TAC.2020.3000819

This article systematically studies consensus of linear multiagent systems (MASs) on directed graphs through adaptive event-triggered control. It presents innovative adaptive event-triggered state-feedback protocols with novel composite event-triggering conditions. Two specific designs in terms of different event-triggering conditions and laws of adaption are first discussed for linear MASs on strongly connected directed graphs, which are then extended to general directed graphs that contain a spanning tree. Moreover, another adaptive event-triggered protocol is proposed for solving leader-follower consensus that tracks a leader of a bounded control input. The protocols inherit the merits of both adaptive control and event-triggered control: the protocols can be implemented in a fully distributed way, since the Laplacian is avoided in design, and each agent only needs to know the relative information between neighbors at discrete instants determined by event-triggering conditions. Compared with the existing related results, the proposed protocols are applicable for linear MASs on general directed graphs, and moreover, the time-dependent term in the event-triggering conditions is allowed to be a class of positive <inline-formula><tex-math notation="LaTeX">L_1</tex-math></inline-formula> functions. Two numerical examples clearly verify the effectiveness of the proposed protocols.