a1 Institute for Mathematics, University of Paderborn, 33095 Paderborn, Germany; firstname.lastname@example.org.
a2 Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK; H.M.Osinga@bristol.ac.uk.
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.
(Received July 22 2003)
(Revised October 30 2003)
(Online publication March 15 2004)
Mathematics Subject Classification: