Low-regret control of singular distributed systems: The Ill-posed backwards heat problem Original Research Article

We use the low-regret notion of Lions [1] for the control of a class of singular distributed systems: the ill-posed problems. A regularization approach is applied to the backwards heat equation, and we obtain a problem of incomplete data, for which the method of Nakoulima et al. [2] is developed. Passing to the limit, a singular optimality system is obtained for the low-regret control of the original problem without any Slater hypothesis.