Control of some linear stochastic systems in a Hilbert space with fractional Brownian motions

Author

Duncan, T.E. ; Maslowski, B. ; Pasik-Duncan, B.

Author_Institution

Dept. of Math., Univ. of Kansas, Lawrence, KS, USA

fYear

2011

fDate

22-25 Aug. 2011

Firstpage

107

Lastpage

110

Abstract

A control problem for a linear system in a Hilbert space with a fractional Brownian motion and a quadratic cost in the state and the control is solved. The feedback form of the optimal control and the optimal cost are given. The optimal control is the sum of the well known linear feedback control for the associated deterministic linear-quadratic control problem and a suitable prediction of an optimal system response to the future noise. Some examples of controlled stochastic partial differential equations are given.

Keywords

Brownian motion; Hilbert spaces; linear systems; optimal control; partial differential equations; state feedback; stochastic systems; Hilbert space; fractional Brownian motions; linear feedback control; linear quadratic control problem; linear stochastic systems; optimal control; optimal cost; optimal system; quadratic cost; stochastic partial differential equations; Brownian motion; Equations; Hilbert space; Mathematical model; Optimal control; Stochastic processes; Stochastic systems; fractional Brownian motion; linear quadratic Gaussian control; linear regulator; linear stochastic systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Methods and Models in Automation and Robotics (MMAR), 2011 16th International Conference on

Conference_Location

Miedzyzdroje

Print_ISBN

978-1-4577-0912-8

Type

conf

DOI

10.1109/MMAR.2011.6031326

Filename

6031326