Summary: We treat the control of distributed systems with missing data following the notion of no regret control used by J.-L. Lions [C. R. Acad. Sci., Paris, Sér. I 315, No. 12, 1253-1257 (1992; Zbl 0766.93033)]. As in [J.-L. Lions, “Duality arguments for multi agents least regret control”, Institut de France (1999), per bibl.], we associate to the no regret control a sequence of least regret controls defined by a quadratic perturbation. Here, we prove that the perturbed system corresponds to a sequence of standard control problems, and converges to the no regret control for which we obtain a singular optimality system. We give also some applications.