On the Regularity of Mayer-Type Affine Optimal Control Problems

The paper presents a sufficient condition for strong metric sub-regularity (SMsR) of the system of first order optimality conditions (optimality system) for a Mayer-type optimal control problem with a dynamics affine with respect to the control. The SMsR property at a reference solution means that any solution of the optimality system, subjected to "small" disturbances, which is close enough to the reference one is at a distance to it, at most proportional to the size of the disturbance. The property is well understood for problems satisfying certain coercivity conditions, which however, are not fulfilled for affine problems.