Open AccessReconstruction of the right-hand part of a distributed differential equation using a positional controlled model
Author(s) -
M. S. Blizorukova,
В. И. Максимов
Publication year - 2020
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm200401
Subject(s) - property (philosophy) , stability (learning theory) , differential equation , mathematics , inverse problem , dynamical systems theory , current (fluid) , inversion (geology) , inverse , class (philosophy) , distributed parameter system , partial differential equation , computer science , mathematical optimization , control theory (sociology) , mathematical analysis , control (management) , artificial intelligence , geometry , paleontology , philosophy , physics , epistemology , quantum mechanics , structural basin , machine learning , electrical engineering , biology , engineering
In this paper, we consider the stable reconstruction problem of the unknown input of a distributed system of second order by results of inaccurate measurements of its solution. The content of the problem considered is as follows. We consider a distributed equation of second order. The solution of the equation depends on the input varying in the time. The input, as well as the solution, is not given in advance. At discrete times the solution of the equation is measured. These measurements are not accurate in general. It is required to design an algorithm for approximate reconstruction of the input that has dynamical and stability properties. The dynamical property means that the current values of approximations of the input are produced on-line, and the stability property means that the approximations are arbitrarily accurate for a sufficient accuracy of measurements. The problem refers to the class of inverse problems. The algorithm presented in the paper is based on the constructions of a stable dynamical inversion and on the combination of the methods of ill-posed problems and positional control theory.