Nonlinear Images of Sets. II: Applications to Differential Games
Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1123-1136
This paper is a continuation of our previous study on weak convexity of nonlinear images of sets [see G. E. Ivanov, Nonlinear images of sets. I: Strong and weak convexity, J. Convex Analysis 27(1) (2020) 363--382]. We consider smoothness of a set in a special sense called "bodily smoothness" and split this smoothness property of a set S into two properties: weak convexity of S and weak convexity of the closure of the complementary to S. We obtain sufficient conditions for bodily smoothness of the image of the Cartesian product of two sets S × U, wherein S is bodily smooth and U is strongly convex. We apply this result for nonlinear differential games and obtain sufficient conditions for the game reachable sets to be smooth.
Classification :
52A05, 46T20, 49N70
Mots-clés : C1,1 mapping, covering mapping, bi-Lipschitz mapping, strong convexity, weak convexity, Minkowski sum, Minkowski operator, differential game
Mots-clés : C1,1 mapping, covering mapping, bi-Lipschitz mapping, strong convexity, weak convexity, Minkowski sum, Minkowski operator, differential game
@article{JCA_2020_27_4_JCA_2020_27_4_a2,
author = {G. E. Ivanov},
title = {Nonlinear {Images} of {Sets.} {II:} {Applications} to {Differential} {Games}},
journal = {Journal of convex analysis},
pages = {1123--1136},
year = {2020},
volume = {27},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a2/}
}
G. E. Ivanov. Nonlinear Images of Sets. II: Applications to Differential Games. Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1123-1136. http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a2/