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Junge, O.; Osinga, H.:
A set oriented approach to global optimal control.
ESAIM: Control, Optimisation and Calculus of Variations, 10(2):259-270, 2004.

We describe an algorithm for computing the value function for ``all source, single destination'' discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem on a finite graph. The method is illustrated by two numerical examples, namely a single pendulum on a cart and a parametrically driven inverted double pendulum.

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