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Necessary Conditions for Optimal Control of Stochastic Evolution Equations in Hilbert Spaces
Journal article   Peer reviewed

Necessary Conditions for Optimal Control of Stochastic Evolution Equations in Hilbert Spaces

AbdulRahman Al-Hussein
Applied mathematics & optimization, Vol.63(3), pp.385-400
01/06/2011
DOI: https://doi.org/10.1007/s00245-010-9125-6

Abstract

Article Calculus of Variations and Optimal Control; Optimization Control Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical and Computational Physics Simulation Systems Theory Theoretical
We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator. We derive a stochastic maximum principle for this optimal control problem. Our results are achieved by using the adjoint backward stochastic partial differential equation.

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