Séance Séminaire

Séminaire ACSIOM

Generalized characteristic method for Fully Convex impulsive systems

This talk is concerned with Fully Convex optimal control problems. In particular, we are interested in a dual approach to study these kind of problems. Fully Convex optimal control problems have been widely investigated by Rockafellar and collaborators when the Lagrangian is coercive and no state constraints are considered. The aim of this talk is to present some new results on the value function of Fully Convex optimal control problems with state constraints. The novelty of this work is that no coercive assumptions are made, which leads to optimal control problems whose trajectories are arcs of bounded variation rather than merely absolutely continuous. Our approach is based on classical convex analysis, and we establish a LegendreFenchel type equality between the value function of the optimal control problem and its dual. The main result we present in this talk is a characteristic method that allows to describe the time-evolution of the subgradients of the value functions through following trajectories of a Hamiltonian system. This is a joint work with Peter Wolenski from Louisiana State University (USA).