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The methods of dynamical reconstruction of an input in a system of ordinary differential equations

  • Vyacheslav I. Maksimov EMAIL logo
Published/Copyright: August 13, 2020

Abstract

In the paper, for systems described by ordinary differential equations a review of algorithms of dynamical input reconstruction by results of inaccurate observations of its solutions is given. The problem under discussion is referred to the class of dynamical inverse problems. The proposed algorithms are stable with respect to informational noises and computational errors. They are based on the combination of methods of the theory of ill-posed problems and the theory of feedback control. The essence of the methodology underlying the algorithms suggested in the paper consists in the representation of a reconstruction algorithm in the form of a feedback control algorithm for a certain artificial dynamical system, a model; such an algorithm, whose output is the realization of the control in the model, is dynamical by its definition.

MSC 2010: 34A55; 49N45; 93B52

Funding statement: The work was performed as a part of research conducted in the Ural Mathematical Center.

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Received: 2020-04-08
Accepted: 2020-07-30
Published Online: 2020-08-13
Published in Print: 2021-02-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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