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Theory of Hidden Oscillations and Stability of Control Systems
Journal of Computer and Systems Sciences International ( IF 0.6 ) Pub Date : 2020-10-11 , DOI: 10.1134/s1064230720050093
N. V. Kuznetsov

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.



中文翻译:

隐藏振荡理论和控制系统的稳定性

摘要

绝对稳定性理论,分岔理论,混沌理论,鲁棒控制理论以及新的计算技术的发展,使得人们有可能重新审视该领域中许多著名的理论和实践问题。多维控制系统的分析,从而导致了隐性振荡理论的出现,这代表了安德罗诺夫振荡理论的现代时代。隐性振荡的理论基于新的自激或隐性振荡分类。虽然可以通过分析和数值方法有效地研究振荡的自激,但揭示隐藏的振荡需要开发特殊的分析和数值方法,并且有必要确定全局稳定性的确切边界,分析并缩小实现全局稳定性的必要条件和充分条件之间的差距,并区分与这些条件一致的控制系统类别。这项调查讨论了众所周知的理论和工程问题,其中隐藏的振荡(它们的不存在或存在和位置)起着重要的作用。

更新日期:2020-10-11
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