A set oriented approach to global optimal control

Free access article

Issue		ESAIM: COCV Volume 10, Number 2, April 2004


Page(s)		259 - 270
DOI		10.1051/cocv:2004006

ESAIM: COCV, April 2004, Vol. 10, pp. 259-270
DOI: 10.1051/cocv:2004006

A set oriented approach to global optimal control

Oliver Junge¹ and Hinke M. Osinga²

¹ Institute for Mathematics, University of Paderborn, 33095 Paderborn, Germany; junge@upb.de.
² Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK; H.M.Osinga@bristol.ac.uk.

(Received July 22, 2003. Revised October 30, 2003.)

Abstract
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.

Mathematics Subject Classification. 49J53, 49M25, 65K10, 90C39

Key words: Global optimal control, value function, set oriented method, shortest path.

© EDP Sciences, SMAI 2004

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