# Bang-singular optimal control: second order conditions and a shoooting algorithm

## Venerdi' 9 Marzo 2012 - Maria Soledad Aronna

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Venerdi 9 marzo 2012 alle ore 12:15 in aula 2BC30 Maria Soledad Aronna (Universita di Padova) terra` un seminario dal titolo "Bang-singular optimal control: second order conditions and a shoooting algorithm".

-Abstract
In this work we study optimal control problems for systems affine in the control variable. We consider bound constraints on the control, and finitely many equality and inequality constraints on the initial and final state values. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.
Afterwards, we propose a shooting algorithm and we give a sufficient condition for its convergence. We show a link between this sufficient condition and the one obtained above. In some problems, we are able to analyse the stability of the optimal solution under small perturbations and the inversibility of the Jacobian matrix of the shooting function associated to the perturbed problem.
(joint work with J.F. Bonnans, A.V. Dmitruk, P.A. Lotito and P. Martinon)

Rif. int. M. Bardi, C. Marchi, F. Rampazzo