Vortragsankündigung

Gastvortrag von Herrn Dipl.-Math. techn. Klaus Krumbiegel

Abstrakt

In this talk I will give you a brief introduction in linear quadratic optimal control problems governed by partial differential equations. Furthermore, different inequality constraint will be considered.

In the main part of this talk, we consider a linear quadratic optimal control problem with pointwise state constraints and control constraints, where the control acts at the boundary. It is well known that problems with pointwise state constraints inhibit a lot of diffculties since the Lagrange multipliers are in general only Borel measures. Therefore, different regularization concepts are developed in the last years. However, a direct extension of the Lavrentiev regularization concept is not possible since the control is not defined in the domain where the state constraints are given

In order to overcome this difficulty, we regularize the state constraints by introducing a virtual control v. This control acts in the cost functional, the state equation and the regularized state constraints. The effect of regularization is influenced by different parameter functions depending on a regularization parameter ε > 0. Furthermore, we derive an error estimate for the error between the optimal solution of the original problem and the regularized one. Moreover, under some assumptions on the parameter functions we obtain certain convergence rates of the regularization error

We consider several numerical examples illustrating the behaviour of the error for ε->0 and for different choices of the parameter functions.