Identification for Linear Stochastic Distributed Parameter Systems with Boundary/Point Control

Abstract

Some conditions are given for consistency of a family of least squares estimates of some unknown parameters for a linear stochastic distributed parameter system. The distributed parameter system is described by an analytic semigroup with cylindrical white noise and control that occurs only on the boundary or at discrete points. The consistency of the family of estimates is obtained by relating it to an infinite time horizon control problem and studying the asymptotics of a stationary Riccati equation for the control problem.Keywordsidentificationleast squares estimatesstochastic linear distributed parametric systemsconsistency of least squares