PMID: 15244904Jul 13, 2004Paper

Design and robustness of delayed feedback controllers for discrete systems

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Ilan Harrington, Joshua E S Socolar

Abstract

We study a matrix form of time-delay feedback control in the context of discrete time maps of high dimension. In almost all cases where standard proportional feedback control methods can achieve control, time-delay feedback controllers containing only static elements can be designed to achieve identical linear stability properties. Analysis of an example involving a ring of coupled maps that can be controlled at only two sites demonstrates that the time-delay controller equivalent to a standard optimal controller can be equally robust in the presence of noise, except at special points in parameter space where the uncontrolled system has a mode with Floquet multiplier exactly equal to 1. Numerical simulations confirm the results of the analysis.

References

Feb 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S BielawskiP Glorieux
Sep 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D J GauthierJ E Socolar
Oct 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J E SocolarD J Gauthier
Apr 6, 2001·Physical Review Letters·K Pyragas
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I Harrington, J E Socolar
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P ParmanandaV Gáspár

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Citations

Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P Hövel, E Schöll
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Chol-Ung ChoeEckehard Schöll
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Carolyn M BergerDaniel J Gauthier
Jun 29, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Guoning TangGang Hu
Oct 10, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Serhiy YanchukEckehard Schöll

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