Practical Prescribed-Time Bipartite Consensus Tracking Control for Non-Affine Multiagent Systems Under Actuation Faults

In this paper, the practical prescribed-time bipartite consensus tracking problem for non-linear multi-agent systems (MASs) subject to actuation faults and non-affine dynamics is considered. A barrier Lyapunov function (BLF) based adaptive fault-tolerant control protocol is proposed, which is fully distributed in that any global information for the Laplacian matrix is not in need. The key to achieving this is to introduce a novel information hierarchical mechanism, which eliminates the requirement for the global information of the Laplacian matrix. The control result is global in that it is uniform in the initial condition. This is achieved by introducing a piecewise and differentiable time-varying scaling function into the controller design, which also allows the settling time to be explicitly pre-specified. In addition, this work relaxes the communication condition to only contain a directed spanning tree, preventing the restrictive requirement that the signed graph must be structurally balanced as imposed in most existing bipartite consensus works. With the developed control protocol, the bipartite consensus error is ensured to converge to a sufficient small compact set, with all the signals in the closed-loop system remaining bounded.