Stabilization of unstable steady states by variable delay feedback control

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.

7 pages, 4 figures, RevTeX

References in corpus (5)

• On the Mechanism of Time--Delayed Feedback Control
• Control of unstable steady states by time-delayed feedback methods
• Refuting the odd number limitation of time-delayed feedback control
• Control of unstable steady states by extended time-delayed feedback
• Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control

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• Synchronization of networks of oscillators with distributed delay coupling
• Laminar Chaos
• Variable-delay feedback control of unstable steady states in retarded time-delayed systems
• Delayed feedback control of unstable steady states with high-frequency modulation of the delay
• Aging transition in systems of oscillators with global distributed-delay coupling
• Laminar Chaos in experiments and nonlinear delayed Langevin equations: A time series analysis toolbox for the detection of Laminar Chaos
• Laminar chaos in systems with quasiperiodic delay