### 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 language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 9 |

Publication status | Published - 1998 |

Externally published | Yes |

### Publication series

Name | Memorandum |
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Publisher | University 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.