Advances on the extended stochastic rayleigh quotient estimation theory

Abstract

A new extended stochastic Rayleigh quotient estimation theory is developed for the identification of the unknown feedback matrix and nonlinear function parameters of a proposed multivariable plant. Systems tractable to this approach encompass a wide class of nonlinear closed-loop time-variant control models that are observed at two localities in a statistically-known white Gaussian noisy environment. Phases of the estimation problem via a partitioning frame technique are given that yield pragmatical computable solutions. An optimal modified-predictor—corrector maximum-likelihood scheme is delineated for solving the state estimation problem, and its invariance to a priori statistics is investigated. In addition, this article presents the analysis of extended stochastic Rayleigh quotient algorithms, extended SRQA's , for the evaluation of the unknown parameters. Nonlinear programming formulations are treated for the algorithms' commencement. Moreover, a noncyclic adaptive computational procedure is depicted to ensure the pointwise convergence of the extended SRQA's in the mean-square sense. Finally, applicability of the devised theory to a nonlinear third-order system is demonstrated as well as a comparison between different suggested methods.