Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(2): 479-497

Online first article January 8, 2018      Printed March 30, 2018

https://doi.org/10.4134/BKMS.b170083

Copyright © The Korean Mathematical Society.

Optimal control on semilinear retarded stochastic functional differential equations driven by Poisson jumps in Hilbert space

Durga Nagarajan, Muthukumar Palanisamy

The Gandhigram Rural Institute - Deemed University, The Gandhigram Rural Institute - Deemed University

Abstract

This paper deals with an optimal control on semilinear stochastic functional differential equations with Poisson jumps in a Hilbert space. The existence of an optimal control is derived by the solution of proposed system which satisfies weakly sequentially compactness. Also the stochastic maximum principle for the optimal control is established by using spike variation technique of optimal control with a convex control domain in Hilbert space. Finally, an application of retarded type stochastic Burgers equation is given to illustrate the theory.

Keywords: nonlinear optimal control, Poisson jump processes, retarded system, stochastic dynamic system, stochastic maximum principle

MSC numbers: Primary 37L55, 60G57, 93E20