A set oriented approach to global optimal control

Oliver Junge; Hinke M. Osinga

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 10, Issue: 2, page 259-270
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Junge, Oliver, and Osinga, Hinke M.. "A set oriented approach to global optimal control." ESAIM: Control, Optimisation and Calculus of Variations 10.2 (2010): 259-270. <http://eudml.org/doc/90729>.

@article{Junge2010,
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. },
author = {Junge, Oliver, Osinga, Hinke M.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Global optimal control; value function; set oriented method; shortest path.; global optimal control; shortest path},
language = {eng},
month = {3},
number = {2},
pages = {259-270},
publisher = {EDP Sciences},
title = {A set oriented approach to global optimal control},
url = {http://eudml.org/doc/90729},
volume = {10},
year = {2010},
}

TY - JOUR
AU - Junge, Oliver
AU - Osinga, Hinke M.
TI - A set oriented approach to global optimal control
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 10
IS - 2
SP - 259
EP - 270
AB - 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.
LA - eng
KW - Global optimal control; value function; set oriented method; shortest path.; global optimal control; shortest path
UR - http://eudml.org/doc/90729
ER -

References

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