2020/11/16 by Giovanni Fusco, Fusco, Giovanni, Monica Motta +1
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Optimization and Variational Analysis #Stability and Control of Uncertain Systems #math.OC #msc:34K45 #msc:49K15 #msc:49N25
paper · pdf · doi:10.48550/arxiv.2011.07853
arxiv created 2020/11/18 · arxiv updated 2020/11/19
In this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data.