We consider the optimal control of a nonlinear elliptic problem with
missing data (so-called ill-posed problems). Using the notion of
no-regret and low-regret control, we give a characterization of the
control for ill-posed problems. More precisely, we study the control
of Cauchy evolution problems via a regularization approach which
generates incomplete information. We obtain a singular optimality
system characterizing the no-regret control for the Cauchy evolution
problems.

optimal control, no regret, low regret