Optimal Control of Stochastic Systems on Hilbert Space

Author:	Ahmed Nasiruddin, University of Ottawa, Canada
Topic:	2.4 Optimal Control
Session:	Optimal Control in Stochastic Systems
Keywords:	Stochastic Differential Equations,Hilbert Space, Measurable Vector Fields, Finitely Additive MeasureSolutions, Optimal Feedback Controls.

Abstract

This paper is concerned with optimal control of semilinear stochastic evolution equations on Hilbert space driven by stochastic vector measure. Both continuous and discontinuous (measurable) vector fields are admitted. Due to nonexistence of regular solutions, existence and uniqueness of generalized (or measure valued) solutions are proved. Using these results, existence of optimal feedback controls from the class of bounded Borel measurable maps are proved for several interesting optimization problems.