Vector measures applied to optimal control for a class of evolution equations on Banach spaces
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1329-1352
Published online July 6, 2020
Printed October 31, 2020
Nasir Uddin Ahmed
University of Ottawa
Abstract : In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by vector measures. We prove existence and uniqueness of solutions and continuous dependence of solutions on the control measures. Using these results we prove existence of optimal controls for Bolza problems. Based on this result we present necessary conditions of optimality.
Keywords : Systems driven by vector measures, impulsive systems, measures as controls, existence of solutions, existence of optimal controls, necessary conditions of optimality
MSC numbers : Primary 34G20, 34H05, 49J27, 49J55, 93C20
Supported by : This work was nancially supported by National Science and Engineering Research Coun-cil, Canada
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