Chapter 24. Experimental Control of Highly Unstable Systems Using Time Delay Coordinates

  1. Heinz G. Schuster
  1. U. Dressler and
  2. A. Schenck zu Schweinsberg

Published Online: 31 MAY 2006

DOI: 10.1002/3527607455.ch24

Handbook of Chaos Control

Handbook of Chaos Control

How to Cite

Dressler, U. and Schenck zu Schweinsberg, A. (1999) Experimental Control of Highly Unstable Systems Using Time Delay Coordinates, in Handbook of Chaos Control (ed H. G. Schuster), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527607455.ch24

Editor Information

  1. University of Kiel, Institute of Theoretical Physics, Leibnizstr. 15, D-24098 Kiel, Germany

Author Information

  1. Daimler-Benz AG, Research Institute Frankfurt, Goldsteinstraßie 235, D-60528 Frankfurt, Germany

Publication History

  1. Published Online: 31 MAY 2006
  2. Published Print: 23 FEB 1999

ISBN Information

Print ISBN: 9783527294367

Online ISBN: 9783527607457

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Keywords:

  • highly unstable systems;
  • time delay coordinates;
  • OGY control scheme;
  • control vectors;
  • bronze ribbon

Summary

This chapter contains sections titled:

  • Introduction

  • The OGY control scheme

  • Extensions of the OGY-control method

    • Quasicontinuous control for highly unstable systems

    • The OGY control method for time delay coordinates

  • Quasicontinuous control using time delay coordinates

    • Local dynamics in the time delay embedding system

    • Quasicontinuous control formula for time delay coordinates

  • The bronze ribbon - Experimental setup

  • Control vectors from scalar measurements

    • Unstable periodic orbits from recurrent points

    • Linear dynamics of the unperturbed system

    • Dependence on the control parameter

    • The adaptive orbit correction

  • Control experiments – The bronze ribbon

    • Quasicontinuous control of the bronze ribbon with time delay coordinates

    • Tracking of the bronze ribbon experiment

  • Summary and Conclusions