Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems

Abstract

In this article we study optimal control problems for sys- tems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the initial and final values of the state. We investigate singular optimal solutions for this class of problems, for which we obtain second order necessary and sufficient conditions for weak optimality in integral form. We also derive Goh pointwise necessary op- timality conditions. We show an example to illustrate the results