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Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Adaptive Memory Identification of Fractional Order Systems

Discontinuity, Nonlinearity, and Complexity 4(4) (2015) 413--428 | 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 input-output 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 P-type 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 Riemann-Liouville 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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