This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the ﬁnal state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case.

## Citation

NUMERICAL ALGEBRA, CONTROL AND OPTIMIZATION Volume 2, Number 3, September 2012 pp. 511–546 doi:10.3934/naco.2012.2.511 INRIA Research Report N° 7664 (2011) http://hal.inria.fr/inria-00605128/en/