On the regularity and stability of the Mayer‐type convex optimal control problems

This paper is devoted to sufficient condition for Strong Metric sub-Regularity (SMsR for short) of the set-valued mapping corresponding to the local description of Pontryagin maximum principle for the Mayer-type optimal control problems with convexity condition of the Hamiltonian and functional. In particular, stability property of optimal control for the Mayer-type problem has been established for the occasion of a polyhedral control set and entirely bang-bang solution structure. Moreover, based on the sufficiency of SMsR and stability property of optimal control, we give the approximate errors of Euler discretization methods utilized to such problems.