Francesca Angrisani est chercheuse post-doctorale à Sorbonne Université.
Titre : Higher-order conditions beyond first–order optimality in control problems
Résumé : Higher–order conditions of Goh and Legendre–Clebsch type provide variational information beyond first–order analysis, allowing one to show that certain extremals satisfying the Pontryagin Maximum Principle cannot be local minimizers. In the first part of the talk, I will present recent joint work with F. Rampazzo, where higher–order necessary conditions are derived for control-affine systems with merely Lipschitz continuous dynamics. By combining set-valued Lie brackets with the theory of Quasi Differential Quotients, we recover meaningful second- and third-order variational information in a fully nonsmooth setting, extending the classical smooth framework. In the second part, I will outline how this nonsmooth analysis fits into a broader variational program aimed at understanding how higher-order necessary conditions persist under different sources of degeneracy, including state constraints, geometric degeneracies, and nonlocal interactions through measure-dependent dynamics. This perspective is particularly relevant for control and planning problems where first-order optimality conditions alone fail to capture the true variational structure.