On the strong subregularity of the optimality mapping in an optimal control problem with pointwise inequality control constraints

Abstract

This paper presents sufficient conditions for strong metric subregularity (SMsR) of the optimality mapping associated with the local Pontryagin maximum principle for Mayer-type optimal control problems with pointwise control constraints given by a nite number of inequalities Gj(u) 0. It is assumed that all data are twice smooth, and that at each feasible point the gradients G0 j(u) of the active constraints are linearly independent. The main result is that the second-order su cient optimality condition for a weak local minimum is also suf- cient for a version of the SMSR property, which involves two norms in the control space in order to deal with the so-called two-norm-discrepancy. A detailed direct proof is given, which does not rely on abstract results.