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Fixed-time convergent RNNs with logarithmic settling time for time-variant quadratic programming solving with application to repetitive motion planning

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Abstract

In this paper, fixed-time convergent RNNs with logarithmic settling time are proposed for solving time-variant quadratic programming (QP), where the domain of attraction of the RNN models can be reasonably estimated a priori. Two novel activation functions are designed, and the exact expressions of the settling time functions for each given initial condition are given; and upper bounds of the settling times for any given initial condition can be obtained. In addition, the generic activation functions are constructed and analyzed to achieve logarithmic fixed-time settling. The RNNs based on the generic activation function are designed, which have a faster convergence rate and a fixed-time convergence property. By estimating the bound of the settling time function under given initial conditions in the bounded region, the semi-global fixed-time convergence of the RNN model is in turn established. It is shown that the predefined-time convergence of modified RNN models can be assured by adopting the inverse of the bound. Simulation results verify effectiveness of the proposed computing schemes for the time-variant QP problem solving and the repetitive motion planning of a redundant manipulator.

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Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the National Natural Science Foundation of China under Grant 62073291.

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Authors and Affiliations

  1. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China

    Xing Li, Liming Wang, Guomin Zhong & Mingxuan Sun

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  1. Xing Li
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  2. Liming Wang
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  3. Guomin Zhong
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  4. Mingxuan Sun
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Correspondence to Mingxuan Sun.

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Li, X., Wang, L., Zhong, G. et al. Fixed-time convergent RNNs with logarithmic settling time for time-variant quadratic programming solving with application to repetitive motion planning. Neural Comput & Applic 36, 445–460 (2024). https://doi.org/10.1007/s00521-023-09016-8

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  • DOI: https://doi.org/10.1007/s00521-023-09016-8

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