Fixed-time consensus tracking control for second-order multi-agent systems with bounded input uncertainties via NFFTSM

This paper is devoted to the fixed-time consensus tracking control for second-order multi-agent systems with bounded input uncertainties under a weighted directed topology. Firstly, a novel non-singular fixed-time fast terminal sliding mode (NFFTSM) surface with bounded convergence time in regardless of the initial states is designed, and the explicit expression of the settling time is provided. Fair and unprejudiced comparisons show that the proposed NFFTSM has faster convergence performance than most typical terminal sliding modes in the existed results. Subsequently, by employing the proposed NFFTSM, a non-singular fixed-time distributed control protocol for second-order multi-agent systems is designed, which only requires one-hop information of the neighbours without the global topology information and has the advantage of fast convergence performance both in the reaching phase and sliding phase. Rigorous proofs show that the fixed-time consensus tracking control for second-order multi-agent systems can be guaranteed by the proposed distributed control protocol. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed control scheme.