Linear-Quadratic Fractional Gaussian Control

A control problem for a linear stochastic system with an arbitrary fractional Brownian motion and a cost functional that is quadratic in the system state and the control is solved. An optimal control is given explicitly as the sum of a prediction of the future fractional Brownian motion and the well known linear feedback control for the associated deterministic linear-quadratic control problem. The optimal cost is given explicitly using fractional calculus. It is noted that the methods to obtain an optimal control extend directly to other noise processes having finite second moments and continuous sample paths. BIOGRAPHY:Tyrone E. Duncan (M’92-SM’96-F’99) received the BEE degree from Rensselaer Polytechnic Institute in 1963 and the MS and PhD degrees from Stanford University in 1964 and 1967, respectively. He has held regular positions at the University of Michigan (1967-1971), the State University of New York, Stony Brook (1971-1974), and the University of Kansas (1974present) where he is Professor of Mathematics. He has held visiting positions at the University of California, Berkeley (1969-1970), the University of Bonn, Germany (1978-1979), and Harvard University (1979-1980) and shorter visiting positions at numerous other institutions throughout the world. Dr Duncan has done research in stochastic analysis, stochastic control and filtering, information theory, stochastic systems and related topics. Dr. Duncan is a member of the editorial boards of Communications on Stochastic Analysis, and Risk and Decision Analysis and was on the editorial board of SIAM Journal on Control and Optimization (1994-2007) as an Associate Editor and a Corresponding Editor. He is a member of AMS, MAA, and SIAM and an IEEE Fellow. Control Science & Dynamical Systems