Fixed-Time Flocking and Collision Avoidance Problem of a Cucker–Smale Model

Abstract

Multiagent systems are used in artificial intelligence, control theory, and social sciences. In this article, we studied a Cucker–Smale model with a continuous non-Lipschitz protocol. The methodology presented in the current paper is based on the explicit construction of a Lyapunov functional. By using the fixed-time control technology, we show that the flocking can occur in fixed-time and collision avoiding when a singular communication function with a weighted sum of sign functions of the relative velocities among agents, and we can obtain the estimation of the converging time which is independent of the initial states of agents. Theoretical results are supported by numerical simulations.