In this note, we consider an optimal control problem associated to a
differential equation driven by a H\"{o}lder continuous function g of index
greater than 1/2. We split our study in two cases. If the coefficient of dg\_t
does not depend on the control process, we prove an existence theorem for a
slightly generalized control problem, that is we obtain a literal extension of
the corresponding deterministic situation. If the coefficient of dg\_t depends
on the control process, we also prove an existence theorem but we are here
obliged to restrict the set of controls to sufficiently regular functions.Comment: 13 page
