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Controlling Oscillations in Nonlinear Systems with Delayed Output Feedback

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Control of Self-Organizing Nonlinear Systems

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

We discuss the problem of controlling oscillations in weakly nonlinear systems by delayed feedback. In classical control theory, the objective of the control action is typically to drive the system to a stable equilibrium. Here we also study the possibility of driving the system to a stable limit cycle having a prescribed amplitude and frequency, as well as suppressing unwanted oscillations, using partial state information in the feedback. The presence of the delay in the output feedback turns out to play a crucial role in achieving these goals.

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Author information

Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103, Leipzig, Germany

    Fatihcan M. Atay

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  1. Fatihcan M. Atay
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Correspondence to Fatihcan M. Atay .

Editor information

Editors and Affiliations

  1. Inst für Theoretische Physik, Technische Universität Berlin, Berlin, Berlin, Germany

    Eckehard Schöll

  2. Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Sabine H. L. Klapp

  3. Institut für Theoretische Physik, Technische Universität Berlin, Berlin, Germany

    Philipp Hövel

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Atay, F.M. (2016). Controlling Oscillations in Nonlinear Systems with Delayed Output Feedback. In: Schöll, E., Klapp, S., Hövel, P. (eds) Control of Self-Organizing Nonlinear Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-28028-8_4

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