Identification of input nonlinear control autoregressive systems using fractional signal processing approach

Area of Science:

• Signal Processing
• Control Systems Engineering
• Nonlinear System Identification

Background:

• Input nonlinear control autoregressive (INCAR) models are crucial for representing complex dynamic systems.
• Accurate parameter estimation is essential for effective control and analysis of these models.
• Existing methods like Volterra least mean square (VLMS) and kernel least mean square (KLMS) have limitations in performance and convergence.

Purpose of the Study:

• To develop a novel algorithm for parameter estimation of INCAR models.
• To introduce a fractional signal processing approach for enhanced model adaptation.
• To compare the performance of the proposed algorithm against established methods.

Main Methods:

• Parameterization of INCAR systems to achieve linear-in-parameter models.
• Application of the fractional least mean square (FLMS) algorithm for adaptive parameter estimation.
• Performance evaluation using convergence analysis against third-order Volterra least mean square (VLMS) and kernel least mean square (KLMS) algorithms.

Main Results:

• The proposed FLMS algorithm exhibits superior accuracy in parameter estimation compared to VLMS and KLMS.
• FLMS demonstrates enhanced convergence properties for INCAR models.
• The algorithm's effectiveness is validated across a range of signal-to-noise ratios, from low to high.

Conclusions:

• The novel FLMS algorithm offers a more accurate and convergent solution for parameter estimation in INCAR models.
• Fractional signal processing provides a robust framework for adaptive filtering in nonlinear systems.
• The proposed method outperforms traditional VLMS and KLMS algorithms, particularly in challenging signal conditions.