Nonsmooth Feedback Control for Multi-Agent Dynamics

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.