Chaotic shuffled frog leaping algorithms for parameter identification of fractional-order chaotic systems

ABSTRACT

An accurate mathematical model has a vital role in controlling and synchronisation of chaotic dynamic systems. This paper proposes a shuffled frog leaping (SFL) algorithm and two chaotic versions of it to detect the unknown parameters and orders of chaotic models. The SFL by a grouping search strategy can provide a good exploration of search space. Also an independent local search for each group in this algorithm provides a proper exploitation ability. In the current research, to help the SFL to jump out of the likely local optima and to provide a better stochastic property to increase its convergence rate and resulting precision, the chaotic mapping is incorporated with the SFL. The superiority of the proposed algorithms is investigated on parameter identification of several typical fractional-order chaotic systems. Numerical simulation, comparisons with some typical existing algorithms and non-parametric analysis of obtained results show that the proposed methods have effective and robust performance. A considerably better performance of proposed algorithms based on average of objective functions demonstrates that the proposed idea can evolve robustness and consistence of SFL.

KEYWORDS:

• Chaotic systems
• shuffled frog leaping
• fractional order
• chaotic mapping