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Fixed-Time Flocking Problem of a Cucker–Smale Model

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  • Fen Nie
  • Yicheng Liu

Abstract

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.

Suggested Citation

  • Fen Nie & Yicheng Liu, 2020. "Fixed-Time Flocking Problem of a Cucker–Smale Model," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, May.
    • Handle: RePEc:hin:jnlmpe:7319608
    DOI: 10.1155/2020/7319608
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