On the control of moving sets: Positive and negative confinement results

We consider a few individuals whose task is to confine a moving population. This is a control problem where the state to be controlled is a compact subset of ℝn. We first prove a negative result on the impossibility of confinement, a key assumption being a sufficiently large initial volume. Then a positive result is also provided through the construction of a confining control, when the initial set has a suitable diameter. Numerical integrations show possible behaviors when the above results do not apply. © 2013 Society for Industrial and Applied Mathematics.