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.
@article{arxiv.2203.03865,
title = {A Second-Order Reachable Sets Computation Scheme via a Cauchy-Type Variational Hamilton-Jacobi-Isaacs Equation},
author = {Lekan Molu and Ian Abraham and Sylvia Herbert},
journal= {arXiv preprint arXiv:2203.03865},
year = {2022}
}