Reduction of state dependent sweeping process to unconstrained differential inclusion

In this articlewe discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets.We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state dependent sweeping process with unbounded perturbations. The perturbations are not required to be convex valued.