Stabilization of unstable steady states by variable delay feedback control

Details Stabilization of unstable steady states by variable delay feedback control Stabilization of unstable steady states by variable delay feedback control

2008-05-27

arxiv.org/abs/0805.4064v1

Europhys. Lett. 84, 40013 (2008).

Physics

General Physics

7 pages, 4 figures, RevTeX

Scientific paper

10.1209/0295-5075/84/40013

We report on a dramatic improvement of the performance of the classical time-delayed autosynchronization method (TDAS) to control unstable steady states, by applying a time-varying delay in the TDAS control scheme in a form of a deterministic or stochastic delay-modulation in a fixed interval around a nominal value $T_0$. The successfulness of this variable delay feedback control (VDFC) is illustrated by a numerical control simulation of the Lorenz and R\"{o}ssler systems using three different types of time-delay modulations: a sawtooth wave, a sine wave, and a uniform random distribution. We perform a comparative analysis between the VDFC method and the standard TDAS method for a sawtooth-wave modulation by analytically determining the domains of control for the generic case of an unstable fixed point of focus type.

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