A Set Oriented Approach to Global Nonlinear Optimal Control

Oliver Junge, Universitat Paderborn

We develop a set oriented method for approximating the optimal value function and approximate optimal trajectories of "all source, single destination" discrete-time nonlinear optimal control problems. The idea of the method is to employ a set oriented multilevel approach in order to explicitly construct a weighted directed graph that is a finite state model of the original continuous space control system. On this graph, standard graph theoretic methods for computing (all source, single destination) shortest paths can be applied in order to compute the desired objects. We show that the approximate optimal value function converges pointwise to the true one as the discretization parameter goes to zero. As an example we approximate the optimal value function and approximate optimal trajectories for a single resp. a double controlled inverted pendulum. This is joint work with Hinke Osinga (Bristol).