Tikhonov regularization of control-constrained optimal control problems

Abstract

We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang-bang solutions, we introduce another assumption to obtain the same convergence rates. This new condition turns out to be useful in the derivation of error estimates for the discretized problem. The necessity of the just mentioned assumptions to obtain certain convergence rates is analyzed. Finally, a numerical example confirms the analytical findings.