Fixed-time flocking problem of a Cucker–Smale type self-propelled particle model

Abstract

In this paper, we consider the fixed-time flocking problem of the Cucker–Smale system. We present a variation of the standard Cucker–Smale system, and a simple fixed-time controller is designed. Based on the fixed-time stability theory, sufficient conditions for the system to achieve flocking within fixed time are obtained. Both our theoretical and numerical results demonstrate that the convergence time depends on the group size, and the group with high density can transit to ordered collective motion more rapidly.