Optimal Control of Stochastic Systems Driven by Fractional Brownian Motions
Project Award Date: 07-01-2010
The family of fractional Brownian motions has been identified empirically to be appropriate stochastic models for a wide variety of physical phenomena.The analysis of these processes in models is only in its infancy. The problems of prediction and optimal control for both fmite and infmite dimensional systems driven by fractional Brownian motions will be investigated. Both of these problems are fundamental for the applications of these systems. The infmite dimensional systems are described by stochastic equations in a Hilbert space which can describe stochastic delay and stochastic partial differential equations. The equations to be considered are linear) bilinear, semilinear and nonlinear. While Brownian motion is a member of the family of fractional Brownian motions) all of the other fractional Brownian motions have important properties that are distinct from those for Brownian motion so the prediction and optimal control methods for Brownian motion cannot be used for these other fractional Brownian motions. Methods from stochastic analysis and stochastic control will be used to analyze the prediction and control problems.
Primary Sponsor(s): US Army