"Control of fast Chaos in a Time-Delay Systems"

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)


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.


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Last Modified:  08/12/03