@inproceedings{ber-her-ale-cha-21-aa-control,
  author = {Bertin, Etienne and H{\'e}riss{\'e}, Bruno and Alexandre dit Sandretto, Julien and Chapoutot, Alexandre},
  title = {Spatio-Temporal Constrained Zonotopes for Validation of Optimal Control Problems},
  booktitle = {Proceedings of the 60th IEEE Conference on Decision and Control (CDC)},
  year = 2021,
  month = dec,
  pages = {6708-6713},
  doi = {10.1109/CDC45484.2021.9683301},
  comment = {Calls AA ``operations on zonotopes''. Applies it to systems control.},
  abstract = {A controlled system subject to dynamics with unknown but bounded parameters is considered. The control is defined as the solution of an optimal control problem, which induces hybrid dynamics. A method to enclose all optimal trajectories of this system is proposed. Using interval and zonotope based validated simulation and Pontryagin’s Maximum Principle, a characterization of optimal trajectories, a conservative enclosure is constructed. The usual validated simulation framework is modified so that possible trajectories are enclosed with spatio-temporal zonotopes that simplify simulation through events. Then optimality conditions are propagated backward in time and added as constraints on the previously computed enclosure. The obtained constrained zonotopes form a thin enclosure of all optimal trajectories that is less susceptible to accumulation of error. This algorithm is applied on Goddard’s problem, an aerospace problem with a bang-bang control.}
}