Control of the 1D continuous version of the Cucker-Smale model*

B. Piccoli, Francesco Rossi, E. Trélat
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引用次数: 2

Abstract

The well-known Cucker-Smale model is a microscopic system reproducing the alignment of velocities in a group of autonomous agents. Here, we focus on its mean-field limit, which we call the continuous Cucker-Smale model. It is a transport partial differential equation with nonlocal terms. For some choices of the parameters in the Cucker-Smale model (and the continuous one), alignment is not ensured for some initial configurations, therefore it is natural to study the enforcing of alignment via an external force. We provide a control strategy enforcing alignment for every initial data and acting only on a small portion of the crowd at each time. This is an adapted version of the sparse control for a finite number of agent, that is the constraint of acting on a small number of agents at each time.
cucker - small模型的一维连续版控制*
著名的cucker - small模型是一个微观系统,它再现了一组自主代理的速度排列。这里,我们关注的是它的平均场极限,我们称之为连续cucker - small模型。它是一个具有非局域项的输运偏微分方程。对于cucker - small模型(以及连续模型)中某些参数的选择,对于某些初始配置不能保证对齐,因此研究通过外力强制对齐是很自然的。我们提供了一种控制策略,强制对每个初始数据进行对齐,并且每次只对一小部分人群起作用。这是有限数量代理稀疏控制的一个改编版本,即每次作用于少量代理的约束。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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