A Predefined-Time Adaptive Zeroing Neural Network for Solving Time-Varying Linear Equations and Its Application to...

Area of Science:

• Engineering mathematics
• Computational neuroscience
• Robotics

Background:

• Time-varying linear equations (TVLEs) are crucial in engineering but face challenges with computation time and noise.
• Existing Zeroing Neural Network (ZNN) models offer potential but require improvements in efficiency and robustness.

Purpose of the Study:

• To propose a novel predefined-time adaptive Zeroing Neural Network (PTAZNN) model for solving TVLEs.
• To enhance convergence speed and computational resource utilization compared to existing ZNN models.

Main Methods:

• Development of a PTAZNN model with a unique error-based adaptive parameter.
• Rigorous mathematical analysis of the model's stability, convergence, and robustness.
• Numerical simulations and application to a UR5 robot's inverse kinematics.

Main Results:

• The PTAZNN model demonstrates significantly shorter convergence times than variable-parameter ZNN models.
• The model exhibits superior robustness and noise resistance.
• Successful application to the UR5 robot's inverse kinematics problem in CoppeliaSim.

Conclusions:

• The PTAZNN model effectively addresses limitations of existing methods for TVLEs.
• The adaptive parameter strategy enhances computational efficiency.
• The model shows practical feasibility and potential for real-world engineering applications, including robotics.