Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems
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 p...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/382834 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558520188272640 |
|---|---|
| author | Fei Gao Xue-Jing Lee Heng-qing Tong Feng-xia Fei Hua-ling Zhao |
| author_facet | Fei Gao Xue-Jing Lee Heng-qing Tong Feng-xia Fei Hua-ling Zhao |
| author_sort | Fei Gao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-46dee78f1de4403c8a54ae5442834ae2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-46dee78f1de4403c8a54ae5442834ae22025-02-03T01:32:05ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/382834382834Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic SystemsFei Gao0Xue-Jing Lee1Heng-qing Tong2Feng-xia Fei3Hua-ling Zhao4Department of Mathematics, School of Science, Wuhan University of Technology, Luoshi Road 122, Wuhan, Hubei 430070, ChinaDepartment of Mathematics, School of Science, Wuhan University of Technology, Luoshi Road 122, Wuhan, Hubei 430070, ChinaDepartment of Mathematics, School of Science, Wuhan University of Technology, Luoshi Road 122, Wuhan, Hubei 430070, ChinaDepartment of Mathematics, School of Science, Wuhan University of Technology, Luoshi Road 122, Wuhan, Hubei 430070, ChinaDepartment of Statistics, School of Science, Wuhan University of Technology, Luoshi Road 122, Wuhan, Hubei 430070, ChinaIn 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.http://dx.doi.org/10.1155/2013/382834 |
| spellingShingle | Fei Gao Xue-Jing Lee Heng-qing Tong Feng-xia Fei Hua-ling Zhao Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems Abstract and Applied Analysis |
| title | Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems |
| title_full | Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems |
| title_fullStr | Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems |
| title_full_unstemmed | Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems |
| title_short | Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems |
| title_sort | identification of unknown parameters and orders via cuckoo search oriented statistically by differential evolution for noncommensurate fractional order chaotic systems |
| url | http://dx.doi.org/10.1155/2013/382834 |
| work_keys_str_mv | AT feigao identificationofunknownparametersandordersviacuckoosearchorientedstatisticallybydifferentialevolutionfornoncommensuratefractionalorderchaoticsystems AT xuejinglee identificationofunknownparametersandordersviacuckoosearchorientedstatisticallybydifferentialevolutionfornoncommensuratefractionalorderchaoticsystems AT hengqingtong identificationofunknownparametersandordersviacuckoosearchorientedstatisticallybydifferentialevolutionfornoncommensuratefractionalorderchaoticsystems AT fengxiafei identificationofunknownparametersandordersviacuckoosearchorientedstatisticallybydifferentialevolutionfornoncommensuratefractionalorderchaoticsystems AT hualingzhao identificationofunknownparametersandordersviacuckoosearchorientedstatisticallybydifferentialevolutionfornoncommensuratefractionalorderchaoticsystems |