Theory of Hidden Oscillations and Stability of Control Systems

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Theory of Hidden Oscillations and Stability of Control Systems. / Kuznetsov, N. V.

In: Journal of Computer and Systems Sciences International, Vol. 59, No. 5, 01.09.2020, p. 647-668.

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Kuznetsov, N. V. / Theory of Hidden Oscillations and Stability of Control Systems. In: Journal of Computer and Systems Sciences International. 2020 ; Vol. 59, No. 5. pp. 647-668.

BibTeX

@article{8bda7f93678940a893f9bbae0a233b8f,

title = "Theory of Hidden Oscillations and Stability of Control Systems",

abstract = "Abstract: The development of the theory of absolute stability, the theory of bifurcations, the theory of chaos, theory of robust control, and new computing technologies has made it possible to take a fresh look at a number of well-known theoretical and practical problems in the analysis of multidimensional control systems, which led to the emergence of the theory of hidden oscillations, which represents the genesis of the modern era of Andronov{\textquoteright}s theory of oscillations. The theory of hidden oscillations is based on a new classification of oscillations as self-excited or hidden. While the self-excitation of oscillations can be effectively investigated analytically and numerically, revealing a hidden oscillation requires the development of special analytical and numerical methods and also it is necessary to determine the exact boundaries of global stability, to analyze and reduce the gap between the necessary and sufficient conditions for global stability, and distinguish classes of control systems for which these conditions coincide. This survey discusses well-known theoretical and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.",

keywords = "LOCK-IN RANGES, LYAPUNOV DIMENSION, DYNAMICAL MODEL, LIMIT-CYCLES, COSTAS LOOP, PULL-IN, ATTRACTORS, COUNTEREXAMPLES, COMPUTATION, MULTISTABILITY",

author = "Kuznetsov, {N. V.}",

note = "Funding Information: This work was supported by the Russian Science Foundation (project 19-41-02002, 2019-2021). Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = sep,

day = "1",

doi = "10.1134/S1064230720050093",

language = "English",

volume = "59",

pages = "647--668",

journal = "Journal of Computer and Systems Sciences International",

issn = "1064-2307",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "5",

}

RIS

TY - JOUR

T1 - Theory of Hidden Oscillations and Stability of Control Systems

AU - Kuznetsov, N. V.

N1 - Funding Information: This work was supported by the Russian Science Foundation (project 19-41-02002, 2019-2021). Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - Abstract: The development of the theory of absolute stability, the theory of bifurcations, the theory of chaos, theory of robust control, and new computing technologies has made it possible to take a fresh look at a number of well-known theoretical and practical problems in the analysis of multidimensional control systems, which led to the emergence of the theory of hidden oscillations, which represents the genesis of the modern era of Andronov’s theory of oscillations. The theory of hidden oscillations is based on a new classification of oscillations as self-excited or hidden. While the self-excitation of oscillations can be effectively investigated analytically and numerically, revealing a hidden oscillation requires the development of special analytical and numerical methods and also it is necessary to determine the exact boundaries of global stability, to analyze and reduce the gap between the necessary and sufficient conditions for global stability, and distinguish classes of control systems for which these conditions coincide. This survey discusses well-known theoretical and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.

AB - Abstract: The development of the theory of absolute stability, the theory of bifurcations, the theory of chaos, theory of robust control, and new computing technologies has made it possible to take a fresh look at a number of well-known theoretical and practical problems in the analysis of multidimensional control systems, which led to the emergence of the theory of hidden oscillations, which represents the genesis of the modern era of Andronov’s theory of oscillations. The theory of hidden oscillations is based on a new classification of oscillations as self-excited or hidden. While the self-excitation of oscillations can be effectively investigated analytically and numerically, revealing a hidden oscillation requires the development of special analytical and numerical methods and also it is necessary to determine the exact boundaries of global stability, to analyze and reduce the gap between the necessary and sufficient conditions for global stability, and distinguish classes of control systems for which these conditions coincide. This survey discusses well-known theoretical and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.

KW - LOCK-IN RANGES

KW - LYAPUNOV DIMENSION

KW - DYNAMICAL MODEL

KW - LIMIT-CYCLES

KW - COSTAS LOOP

KW - PULL-IN

KW - ATTRACTORS

KW - COUNTEREXAMPLES

KW - COMPUTATION

KW - MULTISTABILITY

UR - http://www.scopus.com/inward/record.url?scp=85090115513&partnerID=8YFLogxK

U2 - 10.1134/S1064230720050093

DO - 10.1134/S1064230720050093

M3 - Article

AN - SCOPUS:85090115513

VL - 59

SP - 647

EP - 668

JO - Journal of Computer and Systems Sciences International

JF - Journal of Computer and Systems Sciences International

SN - 1064-2307

IS - 5

ER -

ID: 71009283