Laura Poggiolini (Firenze Univ.) Sufficient conditions for strong local optimality in a Bolza with a non smooth cost
Inria (Sophia), Jan. 29 2018, 10:00 (salle Galois Coriolis)
Second order sufficient conditions for strong local optimality of Pontryagin extremals have been provided in quite a number of different situations: Bang-bang extremals, singular extremals, partially singular extremals, as well as for extremals given by some concatenation of bang and singular arcs. The common feature of these cases is that they deal with smooth costs. Here we consider an optimal control problem with a Bolza cost constrained by a control-affine dynamics and with fixed end-points on a fixed finite time horizon. More precisely we consider an integral cost involving the absolute value of the control. Even if all the data of the problem are assumed to be smooth, the presence of an absolute value in the cost causes the presence of the so-called inactivated arcs. We consider the case of an extremal given by the concatenation of a bang, an inactivated and a bang arc, and provide sufficient conditions for its strong-local optimality. The conditions are given in terms of regularity conditions and of the coercivity of the second variation of a finite dimensional subproblem of the given one. The sufficiency of such conditions is proven via Hamiltonian methods.
The result was obtained jointly with Dr. Francesca Carlotta Chittaro, LSIS-Université de Toulon (France).