Optimal control of Maxwell's equations with regularized state constraints

Dr. Irwin Yousept, TU Berlin

6 Dec 2010, 17:00; Location: S4|10-1

In this talk, we consider a state--constrained optimal control problem of Maxwell's equations based on a 'vector potential ansatz' for the control. The pointwise state constraints here play an important role to prevent singularities or to achieve certain $L^p$--regularity of the optimal state. Due to the lack of regularity of the control--to--state mapping, existence of Lagrange multipliers cannot be guaranteed. We therefore approximate the optimal control problem using a Moreau-Yosida type regularization. Then optimality conditions with regular multipliers for the regularized problem can be derived straightforwardly. Further it turns out that the optimal control of the regularized problem enjoys higher regularity which then allows us to establish its convergence towards the optimal control of the unregularized problem. The second part of the talk focuses on the numerical analysis of the regularized optimal control problem. We consider a finite element approximation of the regularized optimal control problem based on N\'ed\'elec's curl--conforming edge elements for the discretization of the control and the state. Then, employing the higher regularity of the optimal control, we establish an a priori error estimate for the discretization error in the $\boldsymbol{H}(\bold{curl})$--norm.

Category: CE Seminar


Technische Universität Darmstadt

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