No Infimum Gap and Normality in Optimal Impulsive Control Under State Constraints

Abstract In this paper we consider an impulsive extension of optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence extended-sense minimizer is a normal extremal for constrained Maximum Principle ensures there no gap between infima original its extension. Furthermore, translate such relation into verifiable sufficient conditions normality in form constraint qualifications. Links infimum have previously been explored problems without This establishes links presence constraints additional ordinary control, locally Lipschitz continuous data.