This article is cited in 1 paper

Estimates of the Rate of Convergence of a Dynamic Reconstruction Algorithm under Incomplete Information about the Phase State

A. S. Mart'yanov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: In this paper, we study a dynamic reconstruction algorithm which reconstructs the unknown unbounded input and all unobservable phase coordinates from the results of measurements of part of the coordinates. An upper and a lower bound for the accuracy of the reconstruction is obtained. We determine the class of inputs for which the upper bound is uniform. We give a condition for optimally matching the algorithm parameters, ensuring the highest order of the upper bound and equating the orders of the upper and lower bounds. Thus, we establish the sharpness of the upper bound.

Keywords: nonlinear dynamical system, dynamic reconstruction algorithm, unobservable phase coordinates, optimal algorithm parameter matching.

UDC: 517.977

Received: 31.05.2006

DOI: 10.4213/mzm3754

 English version: Mathematical Notes, 2007, 82:1, 57–66

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