ADAPTIVE REGULARIZATION AND DISCRETIZATION OF BANG-BANG OPTIMAL CONTROL PROBLEMS

In this article, Tikhonov regularization of control-constrained optimal control problems is investigated. Typically the solutions of such problems exhibit a so-called bang-bang structure. We develop a parameter choice rule that adaptively selects the Tikhonov regularization parameter depending on a posteriori computable quantities. We prove that this choice leads to optimal convergence rates with respect to the discretization parameter. The article is complemented by numerical results.