Hybrid approach for deformable mirror online system identification using RLS algorithm and adaptive forgetting factor optimization

Abstract

In this study, an online system identification (SI) approach based on a recursive least squares algorithm with an adaptive forgetting factor (AFFRLS) is proposed to accurately identify the dynamic behavior of a deformable mirror (DM). Using AFFRLS, an adaptive expression that minimizes a weighted linear least squares cost function relating to the input and output signals is obtained. First, the selected identification signals in COMSOL multi-physics software were applied to the finite element (FE) model of the DM. Then, using the COMSOL Livelink for MATLAB, the values of DM deformations are imported into MATLAB. Subsequently, the system is analyzed and identified online using the AFFRLS algorithm and through the optimization of an adaptive forgetting factor. Finally, for validation, the output values of DM have been evaluated with the output values of the proposed model by applying new input signals in order to find the optimal adaptive forgetting factor parameters. For the first time, in this work, the DM’s dynamics has been identified using the AFFRLS algorithm, which has acceptable accuracy despite some drawbacks. In addition, the results show that the AFFRLS method has a significant dominance in terms of accuracy, simplicity and noise reduction despite the slight decrease in speed due to the high computational load.