Discontinuous control problems for non-convex dynamics and near viability for singularly perturbed control systems

The aim of this paper is to study two classes of discontinuous control problems without any convexity assumption on the dynamics. In the first part we characterize the value function for the Mayer problem and the supremum cost problem using viscosity tools and the notion of εε-viability (near viability). These value functions are given with respect to discontinuous cost functionals. In the second part we obtain results describing the εε-viability (near viability) of singularly perturbed control systems.