Confinement strategies in a model for the interaction between individuals and a continuum

This paper presents the basic analytical theory for a model that describes interactions between a few individuals (or agents) and a population (a continuum), all moving in R n. The agents affect the population, either repelling or attracting it. Their aim is to steer the population toward a given region K ⊂ R n. This can be seen as a control problem where the state of the system is the set occupied by the population. In this paper we solve simple confinement problems, where the agents' task is to keep the population within a given set. Rigorous analytical results as well as numerical computations are presented. © 2012 Society for Industrial and Applied Mathematics.