Non-chattering finite-time and fixed-time flocking of Cucker–Smale systems

Abstract

In this paper, the non-chattering finite/fixed-time flocking problems of Cucker–Smale (C–S) systems are investigated. To address the chattering issue, two novel chattering-free protocols are proposed to achieve the flocking of C–S systems within a finite/fixed time. Using the stability theory of differential equations, sufficient conditions for achieving the flocking are established, and the upper bounds of convergence time are given. The connection between the chattering-free flocking protocols and the classic finite/fixed-time control schemes involving the signum function is shown for the first time. Moreover, we discover a correlation between the settling time and the group size. Finally, the effectiveness of the presented protocols is validated via several simulations.