Low-regret control of singular distributed systems: The ill-posed backwards heat problem

摘要

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. (C) 2004 Elsevier Ltd. All rights reserved.