On the switching behavior of sparse optimal controls for the onedimensional heat equation
Abstract
An optimal boundary control problem for the onedimensional heat equation is considered. The objective functional includes a standard quadratic terminal observation, a Tikhonov regularization term with regularization parameter $\nu$, and the $L^1$norm of the control that accounts for sparsity. The switching structure of the optimal control is discussed for $\nu \ge 0$. Under natural assumptions, it is shown that the set of switching points of the optimal control is countable with the final time as only possible accumulation point. The convergence of switching points is investigated for $\nu \searrow 0$.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 arXiv:
 arXiv:1705.03191
 Bibcode:
 2017arXiv170503191T
 Keywords:

 Mathematics  Optimization and Control