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Robust adaptive fractional-order observer for a class of fractional-order nonlinear systems with unknown parameters

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Abstract

This paper investigates the parameter and state estimation problems for a class of fractional-order nonlinear systems subject to the perturbation on the observer gain. The fractional-order nonlinear systems are linear in the unknown parameters and nonlinear in the states. Based on the equivalent integer-order differential equations, a fractional-order non-fragile observer and two kinds of fractional-order adaptive law are derived by applying the direct Lyapunov approach. The results are systematically obtained in terms of linear matrix inequalities and solved by YALMIP Matlab Toolbox. Two numerical examples with comparative result of two proposed adaptive laws are provided to illustrate the efficiency and validity of the proposed method.

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Acknowledgements

The authors would like to thanks all the anonymous reviewers for their valuable suggestions and insightful comments on this manuscript. This work was supported by Science Startup Foundation of Hainan University (No. KYQD(ZR)1872), Natural Science Foundation of Hainan Province (No. 20156218), Natural science Foundation of China (No. 31460318) and the Innovative Project of Post-graduate of Hainan Province (No. Hys2016-27).

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Hainan University, Haikou, 570228, China

    Kai Chen, Rongnian Tang, Chuang Li & Pengna Wei

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  1. Kai Chen
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  2. Rongnian Tang
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  3. Chuang Li
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  4. Pengna Wei
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Correspondence to Chuang Li.

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Chen, K., Tang, R., Li, C. et al. Robust adaptive fractional-order observer for a class of fractional-order nonlinear systems with unknown parameters. Nonlinear Dyn 94, 415–427 (2018). https://doi.org/10.1007/s11071-018-4368-x

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