Advances on the extended stochastic rayleigh quotient estimation theory

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