Controlling the motion of charged particles in a vacuum electromagnetic field from the boundary

We consider the problem of driving two non-relativistic charged particles in a bounded vacuum electromagnetic field to the same location by applying electromagnetic forces through the boundary of the domain. The dynamics of the particles is modeled by the Maxwell–Lorentz system and the problem is reduced to a boundary feedback control problem. Using the perturbed energy method, we design feedback controllers and prove that the particles under the designed control move to the origin exponentially. The techniques of control design and stability analysis may be potentially applied to control of fusion.