2018/01/12 by Tobias Geiger, Geiger, Tobias, Daniel Wachsmuth +1
Engineering · Computer Science · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Contact Mechanics and Variational Inequalities
paper · pdf · doi:10.48550/arxiv.1801.04077
In the present work we study the optimal control of an evolution equation with non-smooth dissipation. The solution mapping of this system is non-smooth and hence the analysis is quite challenging. Our approach is to regularize the dissipation via approximation by a smooth function. We derive optimality conditions for the corresponding smooth optimal control problem. Then we drive the regularization parameter to zero and obtain necessary optimality conditions for the original non-smooth problem. However, in this process we lose regularity of the adjoint variables.