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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.
Highlights
Collective motions refers to an orderly movement organized by agents with limited environmental information and simple rules
The celebrated Cucker–Smale model [5] provided a framework to explain the self-organizing behavior in various complex systems, and the model is given by the following ODE system:
We investigated the flocking problem of a modified Cucker–Smale model with continuous non-Lipschitz protocol
Summary
Collective motions refers to an orderly movement organized by agents with limited environmental information and simple rules. When the influence function has a singular interval, the system will undergo a flocking evolution in finite time, and the minimum distance between agents in the flocking evolution process is greater than the control parameter. Finite-time flocking performance has favourable properties, the estimation of convergence time usually depends on initial states of networked particles. It will restrict the applications in practice if the initial conditions are unavailable previously. There is little work about the fixed-time flocking performance of the Cucker–Smale model. E main purpose of this article is to investigate the fixed-time flocking performance of a Cucker–Smale model.
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