Exploring nonlinearity by feedback

Alexander L. Fradkov

Research output: Book/ReportReportProfessional

Abstract

The possibilities of studying nonlinear physical systems by small feedback action are discussed. Analytical bounds of possible system energy change by feedback are established. It is shown that for 1-DOF nonlinear oscillator the change of energy by feedback can reach the limit achievable for linear oscillator by harmonic (nonfeedback) action. The results are applied to different physical problems: evaluating the amplitude of action causing the escape from a potential well; stabilizing unstable modes of nonlinear oscillator (pendulum); using feedback testing signals in spectroscopy. These and related investigations are united by similarity of goals: studying possibilities and limitations of changing system behavior by feedback and by unified methodology borrowed from cybernetics (control science). They therefore constitute a part of physics which can be called {\em cybernetical physics}.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages9
Publication statusPublished - 1998
Externally publishedYes

Publication series

NameMemorandum
PublisherUniversity of Twente, Faculty of Applied Mathematics
No.1447
ISSN (Print)0169-2690

Keywords

  • MSC-93D30
  • MSC-70H05
  • MSC-58F05
  • MSC-93C10

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  • Cite this

    Fradkov, A. L. (1998). Exploring nonlinearity by feedback. (Memorandum; No. 1447). Enschede: University of Twente, Department of Applied Mathematics.