@misc{StefanelliWachsmuthWachsmuth, author = {Stefanelli, Ulisse and Wachsmuth, Daniel and Wachsmuth, Gerd}, title = {Optimal control of a rate-independent evolution equation via viscous regularization}, series = {Discrete and Continuous Dynamical Systems - Series S (DCDS-S)}, volume = {10}, journal = {Discrete and Continuous Dynamical Systems - Series S (DCDS-S)}, number = {6}, issn = {1937-1632}, doi = {10.3934/dcdss.2017076}, pages = {1467 -- 1485}, abstract = {We study the optimal control of a rate-independent system that is driven by a convex quadratic energy. Since the associated solution mapping is non-smooth, the analysis of such control problems is challenging. In order to derive optimality conditions, we study the regularization of the problem via a smoothing of the dissipation potential and via the addition of some viscosity. The resulting regularized optimal control problem is analyzed. By driving the regularization parameter to zero, we obtain a necessary optimality condition for the original, non-smooth problem.}, language = {en} }