LINEAR-QUADRATIC CONTROL FOR STOCHASTIC EQUATIONSIN A HILBERT SPACE WITH FRACTIONAL BROWNIAN MOTIONS

摘要

A linear-quadratic control problem with a finite time horizon for some infinitedimensionalcontrolled stochastic differential equations driven by a fractional Gaussian noise is formulatedand solved. The feedback form of the optimal control and the optimal cost are givenexplicitly. The optimal control is the sum of the well-known linear feedback control for the associateddeterministic inear-quadratic control problem and a suitable prediction of the adjoint optimalsystem response to the future noise. The covariance of the noise as well as the control operator in thesystem equation can in general be unbounded, so the results can also be applied where the noise orthe control are on the boundary of the domain or at discrete points in the domain. Some examplesof controlled stochastic partial differential equations are given.