Tensor-based predictive control for extremely large-scale single conjugate adaptive optics.

Area of Science:

• Optical Engineering
• Control Systems
• Data Science

Background:

• Large-scale adaptive optics (AO) systems require efficient wavefront sensing and control.
• Traditional methods often struggle with the high dimensionality and complex spatial-temporal dynamics of AO data.
• Predictive control algorithms are crucial for real-time compensation in AO.

Purpose of the Study:

• To propose a novel data-driven predictive control algorithm for large-scale single conjugate adaptive optics systems.
• To develop a method for modeling the spatial-temporal dynamics of wavefront sensor data using tensor-based autoregressive models.
• To reduce computational complexity and improve prediction accuracy in AO systems.

Main Methods:

• Shuffling Shack-Hartmann wavefront sensor data into a d-dimensional tensor.
• Modeling spatial-temporal dynamics using a d-dimensional autoregressive model with multilinear transformations.
• Employing an Alternating Least Squares algorithm to identify factor matrices from open-loop sensor data.
• Parametrizing coefficient matrices using a sum of Kronecker products for efficient representation.

Main Results:

• The proposed tensor-based autoregressive model significantly reduces computational complexity from O(pN^4) to O(prd N^(2(d+1)d)).
• The method achieves high data compression rates by accurately decomposing large-scale autoregressive models.
• Validation on a laboratory testbed shows reduced temporal error, especially at high Greenwood frequencies.

Conclusions:

• The data-driven, tensor-based predictive control algorithm offers an efficient and accurate approach for large-scale AO systems.
• This model structure discovers spatial-temporal coupling from data, avoiding prior assumptions.
• The algorithm demonstrates potential for enhanced performance in real-time adaptive optics applications.