Geodesic
A set oriented approach to global optimal control
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 259-270

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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.

DOI : 10.1051/cocv:2004006
Classification : 49J53, 49M25, 65K10, 90C39
Keywords: global optimal control, value function, set oriented method, shortest path 
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     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},
     mrnumber = {2083487},
     zbl = {1072.49014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2004006/}
}
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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

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