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

Dan Goreac (1) , Oana Silvia Serea (2)

1 PS
2 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations

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 ε-viability (near viability). These value functions are given with respect to discontinuous cost functionals. In the second part we obtain results describing the ε-viability (near viability) of singularly perturbed control systems.

Mots clés: Optimal control; Singular perturbations; Near viability; Hamilton-Jacobi-Bellman equations

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Dan Goreac, Oana Silvia Serea. Discontinuous control problems for non-convex dynamics and near viability for singularly perturbed control systems. Nonlinear Analysis: Theory, Methods and Applications, 2010, 73 (8), pp.2699-2713. ⟨10.1016/j.na.2010.06.050⟩. ⟨hal-00727709⟩