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Entropy 2013, 15(5), 1624-1642; doi:10.3390/e15051624

Genetic Algorithm-Based Identification of Fractional-Order Systems

1,*  and 2
1 Research Institute of Diagnostics and Cybernetics, Xi'an Jiaotong University, Xi'an 710049, China 2 School of Engineering, University of California, Merced, 5200 North Lake Rd., Merced, CA 95343, USA
* Author to whom correspondence should be addressed.
Received: 14 March 2013 / Revised: 23 April 2013 / Accepted: 25 April 2013 / Published: 6 May 2013
(This article belongs to the Special Issue Dynamical Systems)
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Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA) is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems.
Keywords: fractional-order systems; parameter identification; genetic algorithm; output error; noise; excitation fractional-order systems; parameter identification; genetic algorithm; output error; noise; excitation
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhou, S.; Cao, J.; Chen, Y. Genetic Algorithm-Based Identification of Fractional-Order Systems. Entropy 2013, 15, 1624-1642.

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