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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.
Highlights
In recent years, multiagent systems have various applications in widely fields such as biology, robotics, and control theory as well as sociology and economics [1,2,3,4,5,6]
Multiagent dynamical systems are typically fragment for modelling of birds and fishes in nature world, and more and more scientists realized the importance of these models
Consider a model consisting of N autonomous agents. xi (x1i, x2i, . . . , xdi ) ∈ Rd and vi (v1i, v2i, . . . , vdi ) ∈ Rd denote the position and velocity of the i th particle at the time t, respectively, and the modified Cucker–Smale model in this paper can be described by the following equations:
Summary
Multiagent systems have various applications in widely fields such as biology, robotics, and control theory as well as sociology and economics [1,2,3,4,5,6]. In [9], the authors introduced the Cucker–Smale model with a singular communication weight influence function: Mathematical Problems in Engineering ψ(s) s− α. In [24], the authors used singular value influence function (5), through the Lyapunov method, when the initial value lies in the set of the admissible initial configurations can avoid collision. In [26], the authors introduced a Cucker–Smale model with a continuous non-Lipschitz protocol, and the flocking can occur in finite time when the communication rate function is locally Lipschitz continuous and has a lower bound. In [27], the authors introduced a Cucker–Smale model with a continuous nonLipschitz protocol, by constructing a Lyapunov functional to obtain the finite-time flocking, which is the convergence time depending on the initial values.
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