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A set oriented approach to global optimal control

Published online by Cambridge University Press:  15 March 2004

Oliver Junge  and
Hinke M. Osinga
Oliver Junge
Affiliation:
Institute for Mathematics, University of Paderborn, 33095 Paderborn, Germany; junge@upb.de.
Hinke M. Osinga
Affiliation:
Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK; H.M.Osinga@bristol.ac.uk.
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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.

Keywords

Global optimal controlvalue functionset oriented methodshortest path.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 10 , Issue 2 , April 2004 , pp. 259 - 270
Copyright
© EDP Sciences, SMAI, 2004

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