  Motivated by the scalability limitations of Eulerian methods for variational
Hamilton-Jacobi-Isaacs (HJI) formulations that provide a least restrictive
controller in problems that involve state or input constraints under a
worst-possible disturbance, we introduce a second-order, successive sweep
algorithm for computing the zero sublevel sets of a popular reachability value
functional. Under sufficient HJI partial differential equation regularity and
continuity assumption throughout the state space, we show that with state
feedback control under the worst-possible disturbance, we can compute the state
set that are reachable within a prescribed verification time bound.
