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.
|Publication status||Published - 2002|
Additional information: Preprint of a paper later published by EDP Sciences (2004), ESAIM-Control Optimisation and Calculus of Variations, 10(2), pp.259-270, ISSN 1262-3377