Robust prescribed-time coordination control of cooperative-antagonistic networks with disturbances

This article targets at addressing the robust prescribed-time coordination control (PTCC) problems for single-integrator cooperative-antagonistic networks (CANs) with external disturbances under arbitrary fixed signed digraphs without any structural constraints. Toward this end, the PTCC problems for nominal single-integrator CANs without disturbances are first investigated and a fully distributed control protocol with a time-varying gain, which grows to infinity as the time approaches the settling time, is proposed utilizing the relative states of neighboring agents. Then, based on the proposed control protocol for the nominal single-integrator CANs, a new second-order prescribed-time sliding mode control protocol is constructed to achieve accurate PTCC for single-integrator CANs in the presence of external disturbances. Using Lyapunov based analysis, sufficient conditions to guarantee the prescribed-time stability, bipartite consensus, interval bipartite consensus, and bipartite containment of single-integrator CANs without or with disturbances are, respectively, derived. In the end, numerical simulations are given to confirm the derived results.