A Second-Order Reachable Sets Computation Scheme via a Cauchy-Type Variational Hamilton-Jacobi-Isaacs Equation

Abstract: 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.