On a method of estimating chaos control parameters from time series

• Published in: Scientific Bulletin ("Mircea cel Bătrân" Naval Academy) Vol. XXI; no. 2; pp. 19 - 28
• Main Author: Deleanu, D
• Format: Journal Article
• Language: English
• Published: Constanta Naval Academy Publishing House 15.12.2018
• Subjects: Algorithms; Chaos; Chaos theory; Computer simulation; Control; Dynamical systems; Estimating techniques; Estimation; Methods; Parameter estimation; Parameters; Time series
• ISSN: 2392-8956; 1454-864X; 1454-864X; 2392-8956
• DOI: 10.21279/1454-864X-18-I2-002

The algorithm of Ott, Grebogi and Yorke (OGY) is recognized for its efficiency in controlling chaotic dynamical systems, even if the system’s equations are not known and the input data are provided by measured time series in experimental settings. Recently, Santos and Graves (SG) proposed a simple method for estimating the chaos control parameters required by OGY algorithm and applied it to the logistic map. Using only two time series of 100 values, they obtained approximate results for the fixed point case within 2 % of the analytical ones. Although the outputs refer only to a particular case, their conclusion seems to be that the method works as well as in general. To check this statement, we performed a large amount of numerical simulations on different one – dimensional maps. With slight different nuances, our findings were the same so we only presented in the paper the logistic map case. We have noticed that the use of only two short time series implies high risks in a reasonable estimate of the location of the fixed points and of the two control parameters (especially of the second). For large enough number of time series (three or five sets of 400 values each, in the paper) the results provided by numerical simulation approximated the theoretical ones within the limit of a few percent at most. The role played by each method parameter, as the radius for a close encounter of the fixed point or the number of the series and their lengths, is also investigated.