Quadratic order conditions for bang-singular extremals
  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. 
Maria Soledad Aronna (CIFASIS CONICET, INRIA Saclay - Ile de France,   CMAP, CIFASIS), J. Frederic Bonnans (INRIA Saclay - I...
math.OC cs.SY