Fixed-Time Flocking Problem of a Cucker–Smale Model

Abstract EN

In this paper, we studied a Cucker–Smale model with continuous non-Lipschitz protocol.

The methodology presented in the current work 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 if the communication rate function is locally Lipschitz continuous and has a lower bound, 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.