Clarke Subdifferentials of a Minimal Time Function in Normed Spaces

Abstract

In a general normed vector space, we study the minimal time function determined by a differential inclusion where the set-valued mapping involved has constant values of a bounded closed convex set U and by a closed target set S. We show that Clarke subdifferential of aminimal time function are representable by virtue of corresponding normal cones of sublevel set of the function and level or suplevel sets of the support function of U. The known results in the literature was obtained only in Banach space.