Fixed-Time Leader-Following Consensus for Second-Order Multiagent Systems With Input Delay

This paper studies fixed-time leader-following lag consensus problem of second-order multiagent systems with input delay. Using fixed-time distributed observer, we obtain the leader's states for each followers. An extension of the Artstein's reducing transformation is employed to transform the delayed error system into a second-order system without time delay and a novel nonsingular terminal sliding mode protocol is proposed to achieve fixed-time consensus. The presented sliding mode controller can avoid singularity, eliminate chattering, and achieve exact convergence. It is mathematically proved that the presented protocol can achieve exact fixed-time leader-following lag consensus. Moreover, the upper bound of convergence time only depends on observer parameters, controller parameters, network parameters, and delay time, which makes it possible to determine the convergence time offline regardless of initial condition. The presented protocol is applied to coordinated lag tracking control of single-link robotic manipulators and the results validate the effectiveness of the proposed fixed-time protocol.