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Sliding mode control based on U model for nonlinear discrete system with modeling uncertainties

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Abstract

In this paper, the high precision control problem is investigated for the nonlinear discrete system with modeling uncertainties. A new method based on nonlinear U model is proposed for sliding mode control, then based on which a new sliding mode observer is proposed firstly and a new adaptive reaching law is designed. The convergence of the designed sliding mode observer and the reach ability of the designed adaptive reaching law is proved respectively, then based on which and the Lyapunov’s stability theory the stability of the control system is proved. The observation error problem is also discussed, it is shown that the proposed sliding mode observer has a smaller observation error than the traditional method. Finally, two numerical example is given to illustrate the feasibility and superiority of the proposed design scheme.

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Acknowledgements

This work was supported by Heilongjiang Province Nature Science Foundation under Grant No. LC2015024.

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Authors and Affiliations

  1. College of Computer and Control Engineering, Qiqihar University, Qiqihar, 161006, China

    Fengxia Xu, Xiaohui Song, Hongliang Ren & Shanshan Wang

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  1. Fengxia Xu
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  2. Xiaohui Song
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  3. Hongliang Ren
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  4. Shanshan Wang
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Correspondence to Fengxia Xu.

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Xu, F., Song, X., Ren, H. et al. Sliding mode control based on U model for nonlinear discrete system with modeling uncertainties. Cluster Comput 22 (Suppl 3), 7471–7480 (2019). https://doi.org/10.1007/s10586-018-1775-1

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