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.
Durga Nagarajan, Muthukumar Palanisamy
The Gandhigram Rural Institute - Deemed University, The Gandhigram Rural Institute - Deemed University
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
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