TY - JOUR

T1 - Метод преобразования сложных систем автоматического управления к интегрируемой форме

AU - Камачкин, Александр Михайлович

AU - Потапов, Дмитрий Константинович

AU - Евстафьева, Виктория Викторовна

N1 - Publisher Copyright: © 2021 Saint Petersburg State University. All rights reserved.

PY - 2021

Y1 - 2021

N2 - The article considers a class of automatic control systems that is described by a multidimensional system of ordinary differential equations. The right hand-side of the system additively contains a linear part and the product of a control matrix by a vector that is the sum of a control vector and an external perturbation vector. The control vector is defined by a nonlinear function dependent on the product of a feedback matrix by a vector of current coordinates. The authors solve the problem of constructing a matrix of a nonsingular transformation, which leads the matrix of the linear part of the system to the Jordan normal form or the first natural normal form. The variables included in this transformation allow us to vary the system settings, which are the parameters of both the control matrix and the feedback matrix, as well as to convert the system to an integrable form. Integrable form is understood as a form in which the system can be integrated in a final form or reduced to a set of subsystems of lower orders. Furthermore, the sum of the subsystem orders is equal to the order of the original system. In the article, particular attention is paid to cases when the matrix of the linear part has complex conjugate eigenvalues, including multiple ones.

AB - The article considers a class of automatic control systems that is described by a multidimensional system of ordinary differential equations. The right hand-side of the system additively contains a linear part and the product of a control matrix by a vector that is the sum of a control vector and an external perturbation vector. The control vector is defined by a nonlinear function dependent on the product of a feedback matrix by a vector of current coordinates. The authors solve the problem of constructing a matrix of a nonsingular transformation, which leads the matrix of the linear part of the system to the Jordan normal form or the first natural normal form. The variables included in this transformation allow us to vary the system settings, which are the parameters of both the control matrix and the feedback matrix, as well as to convert the system to an integrable form. Integrable form is understood as a form in which the system can be integrated in a final form or reduced to a set of subsystems of lower orders. Furthermore, the sum of the subsystem orders is equal to the order of the original system. In the article, particular attention is paid to cases when the matrix of the linear part has complex conjugate eigenvalues, including multiple ones.

KW - A system's integrable form

KW - Automatic control system

KW - First natural normal matrix form

KW - Jordan's normal matrix form

KW - Multidimensional nonlinear dynamic system

KW - Nonsingular transformation

KW - nonsingular transformation

KW - first natural normal matrix form

KW - automatic control system

KW - a system's integrable form

KW - multidimensional nonlinear dynamic system

UR - http://www.scopus.com/inward/record.url?scp=85111968891&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3e079b0a-337c-39af-90be-d4f46ea43e53/

U2 - 10.21638/11701/spbu10.2021.209

DO - 10.21638/11701/spbu10.2021.209

M3 - статья

AN - SCOPUS:85111968891

VL - 17

SP - 196

EP - 212

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 2

ER -