@article{17309,
  author = {Paul Manns and Thomas Surowiec},
  title = {On binary optimal control in $H^s(0,T)$, $s < 1/2$},
  abstract = {The function space $H^s(0, T)$, $s \< 1/2$, allows for functions with jump discontinuities and is thus attractive for optimal control problems with discrete-valued control functions. We show that while arbitrary chattering controls are impossible, there exist feasible controls in $H^s(0, T)$ that have countably jump discontinuities with jump height one in each of countably many pairwise disjoint intervals. However, under mild assumptions, we show that such controls cannot be optimal. The derivation of meaningful optimality conditions via a direct variational argument using simple feasible perturbations remains a major challenge; as illustrated by an example.},
  year = {2023},
  journal = {Comptes Rendus Math{\'e}matique},
  volume = {361},
  pages = {1531-1540},
  publisher = {French Academy of Sciences},
}