Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems

Abstract and Applied Analysis

Research Article

Hua-ling Zhao¹  Feng-xia Fei²  Heng-qing Tong²  Xue-Jing Lee²  Fei Gao² 

[1] Department of Statistics, School of Science, Wuhan University of Technology, Luoshi Road 122, Wuhan, Hubei 430070, China, whut.edu.cn;Department of Mathematics, School of Science, Wuhan University of Technology, Luoshi Road 122, Wuhan, Hubei 430070, China, whut.edu.cn

Others  :  1296856
DOI  :  10.1155/2013/382834

 received in 2013-05-01, accepted in 2013-10-08,  发布年份 2013

【 摘 要 】

In this paper, a non-Lyapunov novel approach is proposed to estimate the unknown parameters and orders together for noncommensurate and hyper fractional chaotic systems based on cuckoo search oriented statistically by the differential evolution (CSODE). Firstly, a novel Gaos’ mathematical model is proposed and analyzed in three submodels, not only for the unknown orders and parameters’ identification but also for systems’ reconstruction of fractional chaos systems with time delays or not. Then the problems of fractional-order chaos’ identification are converted into a multiple modal nonnegative functions’ minimization through a proper translation, which takes fractional-orders and parameters as its particular independent variables. And the objective is to find the best combinations of fractional-orders and systematic parameters of fractional order chaotic systems as special independent variables such that the objective function is minimized. Simulations are done to estimate a series of noncommensurate and hyper fractional chaotic systems with the new approaches based on CSODE, the cuckoo search, and Genetic Algorithm, respectively. The experiments’ results show that the proposed identification mechanism based on CSODE for fractional orders and parameters is a successful method for fractional-order chaotic systems, with the advantages of high precision and robustness.

【 授权许可】

CC BY   
Copyright © 2013 Fei Gao et al. 2013

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