Surveillance Guidance of Crowds via Lagrangian Controls
摘要
In this paper a general control system representing a set of agents monitoring and guiding a crowd is formulated. Three specific applications are considered: traffic management via autonomous vehicles, crowd surveillance and guidance via drones, and monitoring and influencing opinion dynamics. Mathematically, a multiscale optimal control problem is defined coupling the agents’ dynamic at microscopic level with the general crowd dynamics at macroscopic level. The former consists of controlled ordinary differential equations while the latter of an evolution equation for measures. The cost function includes terms representing the surveillance and guidance effectiveness, as well as the control costs. General conditions are stated to prove existence of optimal controls, which are then verified for the three specific applications.