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Title: On an Algorithmfor the Reconstruction of a Perturbation in a Nonlinear System
Authors: Maksimov, V. I.
Issue Date: 2020
Publisher: Krasovskii Institute of Mathematics and Mechanics
Krasovskii Institute of Mathematics and Mechanics UB RAS
Citation: Maksimov V. I. On an Algorithmfor the Reconstruction of a Perturbation in a Nonlinear System / V. I. Maksimov // Trudy Instituta Matematiki i Mekhaniki UrO RAN. — 2020. — Vol. 26. — Iss. 1. — P. 156-166.
Abstract: A problem of reconstruction of an unknown perturbation in a system of nonlinear ordinary differential equations is considered. The methods of solution of such problems are well known. In this paper we study a problem with two peculiarities. First, it is assumed that the phase coordinates of the dynamical system are measured (with error) at discrete sufficiently frequent times. Second, the only information known about the perturbation acting on the system is that its Euclidean norm is square integrable; i.e., the perturbation can be unbounded. Since the exact reconstruction is impossible under these assumptions, we design a solution algorithm that is stable under information noise and computation errors. The algorithm is based on the combination of elements of the theory of ill-posed problems with the extremal shift method known in the theory of positional differential games. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved.
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85090523742
PURE ID: 12459071
ISSN: 0134-4889
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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