  In this paper, we study the controllability of the two-dimensional
relativistic Vlasov-Maxwell system in a torus, by means of an interior control.
We give two types of results. With the geometric control condition on the
control set, we prove the local exact controllability of the system in large
time. Our proof in this case is based on the return method, on some results on
the control of the Maxwell equations, and on a suitable approximation scheme to
solve the non-linear Vlasov-Maxwell system on the torus with an absorption
procedure. Without geometric control condition, but assuming that a strip of
the torus is contained in the control set and under certain additional
conditions on the initial data, we establish a controllability result on the
distribution function only, also in large time. Here, we need some additional
arguments based on the asymptotics of the Vlasov-Maxwell system with large
speed of light and on our previous results concerning the controllability of
the Vlasov-Poisson system with an external magnetic field [14].
