Stabilization of unstable steady states by variable delay feedback control
Journal
EPL (Europhysics Letters)
Date Issued
2008-05-27
Author(s)
Viktor Urumov
DOI
10.1209/0295-5075/84/40013
Abstract
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.
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.