Integral operators for the reconstruction of the phase vector of dynamical systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0972.93006
publication date: 2001-07-30T00:00:00Z
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 65L09
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 1626582
zbMATH Keywords: nonlinear analytical dynamical systems
zbMATH Keywords: prediction
zbMATH Keywords: observability
zbMATH Keywords: reconstruction of the phase vector
zbMATH Keywords: uniqueness
zbMATH Keywords: observable functions
zbMATH Keywords: control
zbMATH Keywords: duality principle
author: Yu. V. Zaika
MaRDI profile type: Publication
title: Integral operators for the reconstruction of the phase vector of dynamical systems
published in: Trudy Petrozavodskogo Gosudarstvennogo Universiteta. Seriya Matematika
review text: The author considers the nonlinear analytical dynamical systems NEWLINE\[NEWLINEdx/dt=f(x(t)),\quad y=g(x(t)),\quad f\in C^\omega(U,\mathbb R^n), \quad g\in C^\omega(U,\mathbb R^1).NEWLINE\]NEWLINE The initial data are unknown. The interval of observation \([0,T]\) and the set of possible finite states \(\{x(T)\}\subseteq U\) in the phase space \(\mathbb R^n\) are given. The problem consists in the construction of the operation enabling any possible realizations of a device to determine uniquely the unknown phase vector. In function dependence terms, a description of observable functions is obtained. An analogue of the duality principle in linear systems is developed for the nonlinear case.
description: scientific article; zbMATH DE number 1626582