Noise-resistant predefined-time convergent ZNN models for dynamic least squares and multi-agent systems

Area of Science:

• Computational neuroscience
• Numerical analysis
• Control theory

Background:

• Zeroing Neural Networks (ZNNs) are effective for dynamic matrix equations.
• Their performance degrades under numerical instability and noise, especially in unequal matrix dimensions.
• Dynamic Least Squares (DLS) problems are particularly sensitive to these challenges.

Purpose of the Study:

• To propose a robust ZNN model for DLS problems under noisy and unstable conditions.
• To enhance numerical stability, precision, and convergence speed.
• To develop a noise-resistant consensus protocol for multi-agent systems.

Main Methods:

• Integration of QR decomposition into the ZNN framework (QRDN-ZNN).
• Introduction of a novel activation function (N-Af) for improved performance.
• Theoretical analysis and experimental validation.

Main Results:

• QRDN-ZNN demonstrates superior noise resistance and accuracy compared to existing ZNN models.
• The N-Af provides higher accuracy and faster convergence than other state-of-the-art activation functions.
• A novel noise-resistant consensus protocol was developed and validated.

Conclusions:

• The QRDN-ZNN model effectively addresses numerical instability and noise in DLS problems.
• The proposed model offers significant improvements in accuracy and convergence.
• The QRDN-ZNN-inspired consensus protocol enables reliable multi-agent coordination in noisy environments.