We investigate a control problem with a large number of agents – a crowd. This multi-agent system is modelized by a set, each point of which is the position of an agent. The corresponding dynamical system has two-level dynamics: a microscopic one, which concerns the evolution of each agent; a macroscopic one, which describes the evolution of the whole crowd of agents. The state variable of the system is the set of all positions of the agents. Our main contribution consists in introducing and studying suitable concepts for generalizing feedback controls of such multi-agent control systems, involving Filippov type regularization of nonsmooth feedbacks.

中文翻译：

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多智能体动力学的非平滑反馈控制

我们调查了具有大量代理人（人群）的控制问题。该多主体系统由一组模型建模，该集合的每个点都是主体的位置。相应的动力学系统具有两个层次的动力学：微观的动力学，它涉及到每个代理的演化。宏观的，描述整个代理群体的演变。系统的状态变量是代理的所有位置的集合。我们的主要贡献在于引入和研究适用于推广这种多主体控制系统的反馈控制的合适概念，包括非平滑反馈的Filippov类型正则化。