15 Aprile, 2014 11:00 oclock

Seminario Matematico e Fisico di Milano

Second order necessary optimality condistions in optimal control

Helene Frankowska, Université Pierre et Marie Curie (Paris 6)

Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9 - Sala Consiglio 7° piano

Optimal control theory is an active area of research in both mathematics and engineering sciences. Still, many mathematically challenging problems related to second order optimality conditions remain open, mostly because the structural properties of control systems do not fit well the framework of contemporary optimization literature. In this talk I will discuss second-order necessary optimality conditions in deterministic optimal control from the point of view of second order variational analysis. The new approach introduces second order jets of set valued maps and second order approximations of differential equations and, more generally, control systems and differential inclusions. Then a second order variational differential inclusion leads to a second order Fermat like rule of optimality. In particular, it allows to obtain a new pointwise second order condition verified by the adjoint state of the maximum principle and opens new questions to be investigated.