The numerical dynamic programming approach of Section 14.5 can be applied to provide optimal steering for virtual any system. To apply it here, the obstacle region is empty. The main drawback, however, is that the computational cost is usually too high, particularly if the dimension of is high. On the other hand, it applies in a very general setting, and Lie group symmetries can be used to apply precomputed trajectories from any initial state. This is certainly a viable approach with systems for which the state space is or .