Strong and Weak Convexity in Nonlinear Differential Games ?

摘要

We obtain sufficient conditions for the values of the Minkowski operators to be weakly convex and smooth. These operators play the same role in nonlinear differential games as the Minkowski sum and the Minkowski difference do in linear differential games: they are basic operators in algorithms of computing reachable sets and optimal strategies. We also prove that the signed distance to convex sets is a Lipschitz continuous function of the set with respect to the Hausdorff distance.