We prove existence of solutions to the Cauchy problem for the differential inclusion x E A(x) , when A is cyclically monotone and upper semicontinuous.

Some properties of closed sets which generalize concepts of Convex Analysis are compared and characterized. Some of them have a global character and are concerned with controlling the lack of… Expand

We study the sweeping processes in a Hilbert space which are generated by a closed not necessarily convex moving set. A technique is developed, based on measurability properties of normal cones, in… Expand

Abstract The evolution problem known as sweeping process is considered for a class of nonconvex sets called prox-regular (or ϕ -convex). Assuming, essentially, that such sets contain in the interior… Expand

We consider the problem of reaching a target $S$ within the graph of $C$ subject to the differential inclusion of a Lipschitz set-valued map with closed and (mildly non-)convex values.Expand

We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on the… Expand

This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$.… Expand