Resilient fixed-time bipartite consensus of multi-agent systems with nonlinear dynamics and directed graphs

This article is concerned with the bipartite fixed-time consensus problem for a class of multi-agent systems with nonlinear dynamics and directed graphs. To achieve the fixed-time consensus, a discontinuous control protocol is proposed. Compared to the protocols with undirected graphs, the control parameters are designed using a new Laplacian matrix based on an underlying undirected graph. Besides, to apply the method to the multi-agent systems with malicious agents, the proposed controller is combined with the Weighted Mean Subsequence Reduced (WMSR) algorithm which is modified for signed graphs. Finally, some simulations are presented to demonstrate the performance of the proposed method.