Adaptive Bipartite Time-Varying Formation Control for Multi-Agent Systems on Directed Graph

Distributed bipartite time-varying formation control for multi-agent systems with a leader of unknown input on directed graphs is investigated. An adaptive non-smooth protocol proposed in this paper only utilizes the local output feedback information among neighboring agents and thus can avoid using eigenvalue information of the Laplacian matrix of the graph. It is shown that if the directed interaction network containing a spanning tree with the leader as the root is structurally balanced, then the bipartite time-varying formation tracking can be achieved with a leader of bounded input via the proposed scheme. A convergence analysis of the proposed protocol for multi-agent systems is reflected by the Lyapunov method. Finally, a validly numerical simulation is illustrated to show the performance of the proposed scheme.