Geodesic
Algorithms for computing Minkowski operators and their application in differential games
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 2, pp. 224-255 
P. E. Dvurechensky; G. E. Ivanov. Algorithms for computing Minkowski operators and their application in differential games. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 2, pp. 224-255. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Minkowski operators are considered, which extend the concepts of the Minkowski sum and difference to the case where one of the summands depends on an element of the other term. The properties of these operators are examined. Convolution methods of computer geometry and algorithms for computing the values of the Minkowski operators are developed. These algorithms are used to construct epsilon-optimal control strategies in a nonlinear differential game with a nonconvex target set. The errors of the proposed algorithms are estimated in detail. Numerical results for the conflicting control of a nonlinear pendulum are presented.

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