Metaheuristic optimization-based identification of fractional-order systems under stable distribution noises

This research investigates the identification problem of fractional-order chaotic systems under stable distribution noises. A powerful metaheuristic optimization method called composite differential evolution is used for the identification of the fractional-order Lorenz and Chen systems in the noisy environment, where the structure, parameters, orders and initial values of the systems are all unknown. The identification accuracy is examined when the noise follows the three special cases of stable distributions, i.e., Gaussian, Cauchy and Lévy distributions. In addition, the impact of the four parameters of stable distributions on the identification accuracy is discussed. The experimental results show that the identification error becomes larger when the noise switches from Gaussian to Cauchy and Lévy distributions. The results also turn out that the location of the stable distribution noise plays the most substantial role in the identification accuracy.