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Adaptive Sampled-Data Observer Design for a Class of Nonlinear Systems with Unknown Hysteresis

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Abstract

In this paper, a novel adaptive sampled-data observer design is studied for a class of nonlinear systems with unknown Prandtl–Ishlinskii hysteresis and unknown unmatched disturbances based on radial basis function neural networks (RBFNNs). To begin with, we investigate a sampled-data nonlinear system and present sufficient conditions such that the sampled-data nonlinear system is ultimately uniformly bounded (UUB). Then, an adaptive sampled-data observer is designed to estimate the unknown states of the nonlinear system. The unknown hysteresis and the unknown disturbances are approximated by RBFNNs. We also give the learning laws of the weights of RBFNNs, and prove that the estimation errors of the states and the weights are UUB, based on the obtained sufficient conditions and a special constructing Lyapunov–Krasovskii function. Finally, the effectiveness of the proposed design method is verified by numerical simulations.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61374028).

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Authors and Affiliations

  1. College of Electrical Engineering and New Energy, China Three Gorges University, Yichang, 443002, Hubei, China

    Pengpeng Li & Yanjun Shen

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  1. Pengpeng Li
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  2. Yanjun Shen
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Correspondence to Yanjun Shen.

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Li, P., Shen, Y. Adaptive Sampled-Data Observer Design for a Class of Nonlinear Systems with Unknown Hysteresis. Neural Process Lett 52, 561–579 (2020). https://doi.org/10.1007/s11063-020-10275-y

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