Positive Consensus of Directed Multiagent Systems

• Published in: IEEE transactions on automatic control Vol. 67; no. 7; pp. 3641 - 3646
• Main Authors: Liu, Jason J. R., Yang, Nachuan, Kwok, Ka-Wai, Lam, James
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Communication; Cooperative control; Directed graphs; Eigenvalues; Eigenvalues and eigenfunctions; Graph theory; Graphs; Iterative algorithms; Iterative methods; Laplace equations; Linear matrix inequalities; Linear systems; Multi-agent systems; Multiagent systems; Network topology; positive consensus; positive linear systems; System theory; Systems theory; Topology
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3108517

This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent system are described by directed graphs each containing a spanning tree, which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary, and sufficient conditions on positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results.