L. Illing, J. N. Blakely, and Daniel J. Gauthier
(Department Physics and Center for Nonlinear and Complex Systems,
Duke University,
Box 90305, Durham, NC 27708, USA)
Abstract
Controlling fast chaos is challenging because of the inevitable time-lag between
the sensing of the state of the system and the application of the control, that
is, because of control-loop latency. We have discovered that it is possible to
avoid the problem of control-loop latency for time-delay dynamical systems. In t
ime-delay systems it is possible to measure the current state and to apply the c
ontrol perturbation at distinct points in the delay loop, which allows successfu
l control using schemes that are both simple and can tolerate control-loop laten
cies. We demonstrate this point by stabilizing experimentally a periodic orbit
of an opto-electronic time-delay system exhibiting fast chaos in both optical fr
equency and amplitude. Control is achieved through a modified form of time-delay
autosynchronization where the control-loop latency is matched to the time-delay
of the opto-electronic system. The control-loop latency is comparable to the ch
aracteristic timescale of the chaotic oscillations, implying that this simple sc
heme does not require the controller to be faster than the system that is contro
lled. Thus, time-delay systems, which are commonly used as sources of high dimen
sional and fast chaos, are as well ideally suited for applications that require
the control of high speed chaotic oscillations.