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ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Numerical Investigation of the Optimal Measurement for a Semilinear Descriptor System with the Showalter-Sidorov Condition: Algorithm and Computational Experiment

Author(s):

Natalia Alexandrovna Manakova

South Ural State University,
Professor of the Department of Equations of Mathematical Physics,
Doctor of Physical and Mathematical Sciences

manakovana@susu.ru

Olga Gavrilova

South Ural State University,
Senior Lecturer of the Department of Equations of Mathematical Physics

gavrilovaov@susu.ru

Ksenia Vladimirovna Perevozchikova

South Ural State University,
Assistant of the Department of Equations of Mathematical Physics

vasiuchkovakv@susu.ru

Abstract:

The article deals with the problem of optimal measurement for a semilinear descriptor system with a distinguished linear part and a nonlinear term unsolved with respect to the derivative of the unknown vector function with the Showalter–Sidorov initial condition. Basing on the methods of the theory of optimal control we found sufficient conditions for the existence of solutions of the optimal measurement problem – the problem of recovering a dynamically distorted signal from a measuring device. An algorithm for finding a numerical solution uses the methods of decomposition, penalty and the Ritz method as well. The algorithm is based on the representation of the measurement components by polynomials of a given degree, which allows reducing the optimal control problem to a computer programming problem with respect to the unknown coefficients of the polynomials. As an example of a sensor we consider Fitz Hugh – Nagumo oscilloscope described by a nonlinear descriptor system. Computational experiments for the considered sensor model are presented.

Keywords

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