Error estimates for the solution of a control constrained Optimal Control Problem with interior penalties

We consider a control constrained Linear Quadratic Optimal Control Problem and a general interior penalty, including the logarithmic penalty, parameterized by ɛ > 0. The purpose of this work is to find an error estimate for the difference between the optimal control solution uɛ of the penalized problem and the optimal solution u0 of the original problem. An application of the Implicit Function Theorem is not possible in this context. Although, we will be able to apply the so called Restoration Theorem to obtain the desired results.