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A new super-predefined-time convergence and noise-tolerant RNN for solving time-variant linear matrix–vector inequality in noisy environment and its application to robot arm

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Abstract

Recurrent neural networks (RNNs) are excellent solvers for time-variant linear matrix–vector inequality (TVLMVI). However, it is difficult for traditional RNNs to track the theoretical solution of TVLMVI under non-ideal conditions [e.g., noisy environment]. Therefore, by introducing a novel nonlinear activation function (NNAF) and time-variant-gain, a new super-predefined-time convergence and noise-tolerant RNN (SPCNT-RNN) is proposed to acquire an online solution to TVLMVI in noisy environment. The difference between SPCNT-RNN and traditional fixed-parameter RNNs (FP-RNNs) is that the error function equation of SPCNT-RNN has NNAF and time-variant-gain coefficient. Due to this difference, the SPCNT-RNN can achieve super-predefined-time convergence in both noise-free and noisy environments, which is superior to that of existing RNNs. The stability, super-predefined-time convergence, and robustness of SPCNT-RNN are theoretically demonstrated. Moreover, the simulation results between various existing RNNs and SPCNT-RNN verify the feasibility, validity, robustness and rapid convergence effect of the proposed SPCNT-RNN.

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Funding

This work was supported in part by the National Natural Science Foundation of China under Grants 62173176, 61863028, 81660299, and 61503177, and in part by the Science and Technology Department of Jiangxi Province of China under Grants 2020ABC03A39, and 20212ABC03A06.

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Authors and Affiliations

  1. School of information engineering, Nanchang University, Nanchang, 330031, China

    Boyu Zheng, Chong Yue, Qianqian Wang & Chunquan Li

  2. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Zhijun Zhang

  3. State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    Junzhi Yu

  4. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing, 100871, China

    Junzhi Yu

  5. Department of Systems and Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada

    Peter X. Liu

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Correspondence to Chunquan Li.

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Zheng, B., Yue, C., Wang, Q. et al. A new super-predefined-time convergence and noise-tolerant RNN for solving time-variant linear matrix–vector inequality in noisy environment and its application to robot arm. Neural Comput & Applic 36, 4811–4827 (2024). https://doi.org/10.1007/s00521-023-09264-8

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