A computational method for non-convex reachable sets using optimal control

A computational method for the approximation of reachable sets for non-linear dynamic systems is suggested. The method is based on a discretization of the interesting region and a projection onto grid points. The projections require to solve optimal control problems which are solved by a direct discretization approach. These optimal control problems allow a flexible formulation and it is possible to add non-linear state and/or control constraints and boundary conditions to the dynamic system. Numerical results for non-convex reachable sets are presented. Possible applications include robust optimal control problems.