Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2020; 35(4): 1329-1352

Online first article July 6, 2020      Printed October 31, 2020

https://doi.org/10.4134/CKMS.c200066

Copyright © The Korean Mathematical Society.

Vector measures applied to optimal control for a class of evolution equations on Banach spaces

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