“…Through Lemma 3.7, (A 4 ) becomes crucial to ensure the validity of (AC) in Theorem 3.6. In particular, the works [44][45][46][47], which analyze continuity properties of extremals with respect to appropriate deformations of some deterministic optimal control problems and which inspired our work, show that the timecontinuity of optimal controls u k for each LOCP ∆ k represents a requirement which is not easy to relax (in particular, see the counterexample in [47, Section 2.3]), especially in the presence of trust-region constraints. Importantly, motivated by regularity results in deterministic optimal control settings (see, e.g., [48, Theorem 3.2]), we reckon that more generic mappings G might yield Lemma 3.7, especially when optimizing over deterministic controls, although we leave the investigation of more general sufficient conditions for the time-continuity of optimal controls u k for each LOCP ∆ k as a future research direction, in that it is out of the scope of this work which again focuses on the properties of accumulations points of the sequence generated by SCP.…”