Discontinuity, Nonlinearity, and Complexity
Adaptive Memory Identification of Fractional Order Systems
Discontinuity, Nonlinearity, and Complexity 4(4) (2015) 413428  DOI:10.5890/DNC.2015.11.005
Yang Zhao; Yan Li; Fengyu Zhou
School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, PR China
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Abstract
This paper deals with a previously ignored problem that how to find the memory (initialization function) of fractional order system by using the recent sampled inputoutput data. A novel and practical strategy is proposed to estimate the initialization function, which adapts to all system parameters but fractional order. To implement this method, a Ptype order learning approach is introduced to identify the system order separably and accurately, thanks to the fractional order sensitivity function. The initialization response is computed through an iterative learning identification strategy that guarantees the accuracy and adaptiveness simultaneously. Along with the estimations of order and initialization response, a practical piecewise identification criterion of initialization function is established by using the least squares and instrumental variable methods. The above strategy is available for both Caputo and RiemannLiouville fractional order systems, where the initial values are applied rather than the initial conditions. Two illustrated examples are provided to support the conclusions.
Acknowledgments
The authors would like to thank all Editors and Reviewers for their organizations and valuable comments. This work is supported by the National Natural Science Foundation of China (61374101,61375084,61104009).
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