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Robust finite-time control of fractional-order nonlinear systems via frequency distributed model

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Abstract

This paper studies the application of frequency distributed model for finite-time control of a class of fractional-order nonlinear systems. Firstly, a class of fractional-order nonlinear systems with model uncertainties and external disturbances are introduced, and a new frequency distributed model with theoretical inference is presented. Secondly, a novel fast terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite-time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional-order nonlinear systems. Finally, two typical examples of three-dimensional nonlinear fractional-order Lorenz system and four-dimensional nonlinear fractional-order Chen system are employed to demonstrate the validity of the proposed method.

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Acknowledgments

This work was supported by the scientific research foundation of the National Natural Science Foundation (Grant Numbers 51509210 and 51479173), the Science and Technology Project of Shaanxi Provincial Water Resources Department (Grant Number 2015slkj-11), the 111 Project from the Ministry of Education of China (No. B12007), Yangling Demonstration Zone Technology Project (2014NY-32).

Conflict of interest

The authors declare that the work is entirely ours and no parts of it are taken from other researchers. And there is no conflict of interests regarding the publication of this article.

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Authors and Affiliations

  1. Department of Electrical Engineering, Northwest A&F University, Yangling, 712100, Shaanxi, People’s Republic of China

    Bin Wang, Junling Ding, Fengjiao Wu & Delan Zhu

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  1. Bin Wang
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  2. Junling Ding
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  3. Fengjiao Wu
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  4. Delan Zhu
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Correspondence to Bin Wang.

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Wang, B., Ding, J., Wu, F. et al. Robust finite-time control of fractional-order nonlinear systems via frequency distributed model. Nonlinear Dyn 85, 2133–2142 (2016). https://doi.org/10.1007/s11071-016-2819-9

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  • DOI: https://doi.org/10.1007/s11071-016-2819-9

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