TY - GEN
T1 - Spatio-temporal constrained zonotopes for validation of optimal control problems
AU - Bertin, Etienne
AU - Herisse, Bruno
AU - DIt Sandretto, Julien Alexandre
AU - Chapoutot, Alexandre
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - 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.
AB - 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.
U2 - 10.1109/CDC45484.2021.9683301
DO - 10.1109/CDC45484.2021.9683301
M3 - Conference contribution
AN - SCOPUS:85126050820
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6708
EP - 6713
BT - 60th IEEE Conference on Decision and Control, CDC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 60th IEEE Conference on Decision and Control, CDC 2021
Y2 - 13 December 2021 through 17 December 2021
ER -