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    Area of Science:

    • Robotics and Control Systems
    • Computational Neuroscience
    • Applied Mathematics

    Background:

    • Time-dependent matrix inversion (TDMI) is a crucial problem in various scientific and engineering disciplines.
    • Existing methods for TDMI often involve high computational costs or complex structures.
    • There is a need for efficient and robust algorithms to solve TDMI problems.

    Purpose of the Study:

    • To introduce a novel dynamic neural network model for addressing the time-dependent matrix inversion (TDMI) problem.
    • To achieve finite-time convergence and strong robustness in solving TDMI.
    • To demonstrate the model's effectiveness through theoretical analysis and simulations.

    Main Methods:

    • Development of a Frobenius norm-based dynamic neural network (FNBDNN) model.
    • Theoretical analysis to prove finite-time convergence properties.
    • Simulation experiments to validate the model's performance and robustness.
    • Application of the FNBDNN model to precise motion control of a two-axis manipulator.

    Main Results:

    • The FNBDNN model successfully solves the TDMI problem with finite-time convergence.
    • The model exhibits strong robustness without relying on integral operations or nonlinear activation functions.
    • Simulation results confirm the validity and superiority of the FNBDNN model compared to existing approaches.
    • Successful application in precise motion control of a two-axis manipulator.

    Conclusions:

    • The proposed FNBDNN model presents an effective and efficient solution for TDMI.
    • The model's simplified structure and low computational cost make it highly practical.
    • The FNBDNN demonstrates significant potential for applications in robotics and control systems.