M. Soledad Aronna

M. Soledad Aronna, Frédéric Bonnans, Bean San Goh

In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.

M. Soledad Aronna

In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate singular optimal solutions for this class of problems. First, we obtain second order necessary and sufficient conditions for weak optimality. Afterwards, we propose a shooting algorithm and show that the sufficient condition above-mentioned is also sufficient for the local quadratic convergence of the algorithm.