On joint identification of the feedback parameters for hyperchaotic systems: An optimization-based approach

We propose an optimization-based scheme for parameter estimation in high-dimensional chaotic systems, and the symbolic time series analysis (STSA) based method is adopted to address the estimation problem. It is shown that, when the system structure and the corresponding time series are known, the STSA-based method works better with respect to the autocorrelation function (ACF) and the mutual information (MI) technologies. Most importantly, the time delay and the feedback strength of two test systems, i.e., the Mackey–Glass system and an external-cavity semiconductor laser system, can be successfully identified using the proposed scheme. To explore the noise immunity, the influence of certain levels of noise on the STSA-based method is tested.

Research highlights
► We explore the parameter estimation in high-dimensional chaotic systems.
► The method is based on the symbolic time series analysis (STSA).
► The Mackey–Glass system and an external-cavity semiconductor laser system are tested.
► Our proposed approach shows better performance with respect to some other methods.
► Also the noise robustness of the STSA-based method is explored.