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arXiv · 0805.4064

Stabilization of unstable steady states by variable delay feedback control

Aleksandar Gjurchinovski·Viktor Urumov
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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 Rössler 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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Aleksandar Gjurchinovski, Viktor Urumov. 2008-05-27. Stabilization of unstable steady states by variable delay feedback control. https://doi.org/10.1209/0295-5075/84/40013

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