Duality in the optimal control of non-well-posed parabolic equations with positive controls

AbstractSome new results on duality in the optimal control of non-well-posed linear parabolic equations with positive distributed or boundary controls are presented. Problems studied include incomplete information and backward systems, and the completely non-well-posed case. The approach presented exploits the fundamental results of J. L. Lions on the optimality system which characterizes the optimal control. The method can also be used to construct dual optimal non-well-posed systems when the controls are unconstrained