Towards faster and robust solution for dynamic LR and QR factorization.

Area of Science:

• Control Systems Engineering
• Computational Mathematics
• Signal Processing

Background:

• Dynamic LR and QR factorization are crucial in control systems but existing methods struggle with noise.
• Current solutions lack sufficient convergence speed and robustness against interference.

Purpose of the Study:

• To develop an advanced neural dynamic model for improved dynamic factorization under noisy environments.
• To enhance model stability and expand application scenarios through a novel integration strategy.

Main Methods:

• Proposed an Adaptive and Robust-Enhanced Neural Dynamic (AREND) model by integrating Dynamic-Coefficient Type (DCT) and Integration-Enhance Type (IET) Zeroing Neural Dynamic (ZND).
• Introduced a Strategy of Integration-Coupling (SIC) to manage multiple error functions, enhancing model stability.
• Conducted theoretical analysis for convergence and robustness, validated by numerical experiments and real-time 3-D Angle of Arrival localization.

Main Results:

• The AREND model significantly improves convergence speed and anti-noise ability compared to existing methods.
• The Strategy of Integration-Coupling (SIC) enhances model stability and broadens its applicability.
• Numerical experiments and real-time 3-D AoA localization confirm the model's accuracy and effectiveness in high-noise conditions.

Conclusions:

• The proposed AREND model offers a superior solution for dynamic LR and QR factorization in noisy control systems.
• The SIC strategy provides a stable and versatile approach for addressing complex error functions.
• AREND demonstrates practical utility and potential for further development in advanced control applications.