Impact of noise and sampling frequency on the control of peak-to-peak dynamics

A chaotic system with a nearly two-dimensional attractor can be modeled by means of its Peak-to-Peak Dynamics (PPD). Such a compact modeling, which is only based on the availability of output time series, is the starting point for designing effective controllers. In previous papers, it has been shown that the method works very well in an ideal situation, namely when the system is not affected by noise and the output can be continuously measured. In this paper, we consider a realistic environment, where the system is affected by process and measurement noise and the output is sampled at a predefined frequency. It will be shown that, in most cases, simple filtering and peak-detection techniques allow one to reconstruct the PPD, and thus to derive effective controllers. This proves that chaos control based on PPD is sufficiently robust with respect to noise and sampling.
KEYWORDS: Chaos control; Reduced models; Peak-to-peak dynamics