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.
Classification : 49J53, 49M25, 65K10, 90C39
Mots clés : global optimal control, value function, set oriented method, shortest path
@article{COCV_2004__10_2_259_0,
author = {Junge, Oliver and Osinga, Hinke M.},
title = {A set oriented approach to global optimal control},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {259--270},
publisher = {EDP-Sciences},
volume = {10},
number = {2},
year = {2004},
doi = {10.1051/cocv:2004006},
zbl = {1072.49014},
mrnumber = {2083487},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2004006/}
}
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 PY - 2004 DA - 2004/// SP - 259 EP - 270 VL - 10 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2004006/ UR - https://zbmath.org/?q=an%3A1072.49014 UR - https://www.ams.org/mathscinet-getitem?mr=2083487 UR - https://doi.org/10.1051/cocv:2004006 DO - 10.1051/cocv:2004006 LA - en ID - COCV_2004__10_2_259_0 ER -
Junge, Oliver; Osinga, Hinke M. A set oriented approach to global optimal control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 259-270. doi : 10.1051/cocv:2004006. http://www.numdam.org/articles/10.1051/cocv:2004006/
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