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Adaptive neural networks control for uncertain parabolic distributed parameter systems with nonlinear periodic time-varying parameter

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Abstract

This paper studies the problem of adaptive neural networks control (ANNC) for uncertain parabolic distributed parameter systems (DPSs) with nonlinear periodic time-varying parameter (NPTVP). Firstly, the uncertain nonlinear dynamic and unknown periodic TVP are represented by using neural networks (NNs) and Fourier series expansion (FSE), respectively. Secondly, based on the ANNC and reparameterization approaches, two control algorithms are designed to make the uncertain parabolic DPSs with NPTVP asymptotically stable. The sufficient conditions of the asymptotically stable for the resulting closed-loop systems are also derived. Finally, a simulation is carried out to verify the effectiveness of the two control algorithms designed in this work.

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Authors and Affiliations

  1. School of Mathematic and Statistics, Xidian University, Xi’an, 710716, China

    YanFang Lei, JunMin Li & AiLiang Zhao

Authors
  1. YanFang Lei
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  2. JunMin Li
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  3. AiLiang Zhao
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Corresponding author

Correspondence to JunMin Li.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 61573013).

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Lei, Y., Li, J. & Zhao, A. Adaptive neural networks control for uncertain parabolic distributed parameter systems with nonlinear periodic time-varying parameter. Sci. China Technol. Sci. 65, 1482–1492 (2022). https://doi.org/10.1007/s11431-021-1971-1

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  • DOI: https://doi.org/10.1007/s11431-021-1971-1

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