A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games

摘要: We describe and implement an algorithm for computing the set of reachable states a continuous dynamic game. The is based on proof that zero sublevel viscosity solution particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation. While alternative techniques have been proposed, game formulation allows treatment nonlinear systems with inputs uncertain parameters. Because equation's defined throughout state space, methods from level literature can be used to generate more accurate approximations than are possible formulations potentially discontinuous solutions. A numerical implementation our described has released web. Its correctness verified through two vehicle, three dimensional collision avoidance example which analytic available.