  We discuss time-optimal control problems for two setups involving globally
driven Rydberg atoms in the blockade limit by deriving the associated
Hamilton-Jacobi-Bellman equations. From these equations, we extract the
globally optimal trajectories and the corresponding controls for several target
processes of the atomic system, using a generalized method of characteristics.
We apply this method to retrieve known results for CZ and C-phase gates, and to
find new optimal pulses for all elementary processes involved in the universal
quantum computation scheme introduced in [Physical Review Letters 131, 170601
(2023)].
