Student Projects

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ROJECT SUMMARY

Adaptive optics (AO) systems are critical in overcoming atmospheric distortions in ground-based telescopes, enabling sharper and more detailed astronomical observations. This project focuses on designing and synthesising a robust, real-time controller for an AO system. By leveraging advanced control theory, the project aims to significantly enhance the performance of AO systems, ensuring reliable correction of wavefront distortions and improving the quality of astronomical images.

BACKGROUND AND MOTIVATION

Telescopes observing through Earth’s atmosphere suffer from distortions caused by turbulent air layers, which degrade image resolution. Adaptive optics counteract this by using deformable mirrors and wavefront sensors to correct for distortions in real-time.

Current AO systems, while effective, face limitations in:

* Handling dynamic, unknown atmospheric conditions.

* Scalability for large telescopes and next-generation systems.

By synthesising a controller tailored to these challenges, this project seeks to push the boundaries of AO performance, paving the way for discoveries in astronomy and astrophysics.

OBJECTIVES

1. Design and develop a robust controller that addresses dynamic atmospheric variations.

2. Validate performance through simulation (and hardware) implementation using an AO testbed.

3. Ensure scalability and adaptability of the controller for different telescopes and operational conditions.

REQUIREMENTS

The project demands a solid academic foundation in control courses, particularly in ‘Advanced Control Systems.’ Proficiency in the frequency domain approach and robust control techniques is especially critical.

Professor(s)
Alireza Karimi, Vaibhav Gupta
Administration
Barbara Marie-Louise Frédérique Schenkel
External
Department of Astronomy, UNIGE, Isaac Dinis, isaac.dinis@unige.ch
Site
ddmac.epfl.ch, la.epfl.ch
ALT

The goal of the project is to study an application of the Koopman operator based control approach. For autonomous systems, Koopman operator theory shows that a nonlinear system can be represented as a linear system in a higher dimensional (possibly infinite dimensional) space. Thus, by lifting a nonlinear system to a higher dimensional space this approach enables the use of tools from linear systems theory for studying nonlinear systems. By using the Koopman operator approach, our goal is to obtain a linear system representation in a high dimensional space and employ linear control design techniques to control the actually nonlinear system.

The lifted system representation will be obtained in a data-driven fashion. As a result of this as well as further structural restrictions, the lifted representation never exactly captures the original system dynamics. Thus, the project will also aim for bounding these errors such that guarantees for the true closed-loop system can be provided by using robust control tools.

For now a pendulum system is considered as the application.

Skills needed:

-Advanced control systems (familiarity with frequency domain approach and robust control)

-Matlab/Simulink, LabVIEW

Comment
Contact: mert.eyuboglu@epfl.ch
Professor(s)
Alireza Karimi
Administration
Mert Eyuboglu
Site
ddmac.epfl.ch, la.epfl.ch
ALT

The goal of this project is to apply the Koopman operator-based modeling and control approach to a 3DOF gyroscope system. Using the Koopman operator, we aim to obtain a linear system representation in a high-dimensional space, enabling the application of linear control design techniques to an inherently nonlinear system. The lifted system representation will be identified in a data-driven manner and validated on the real system. Once this model is validated, a linear controller will be designed in the lifted space and subsequently tested on the actual system.

Skills needed:

-System identification

-Matlab/Simulink, LabVIEW

Comment
Contact: mert.eyuboglu@epfl.ch, vishnu.varadan@epfl.ch
Professor(s)
Alireza Karimi
Administration
Mert Eyuboglu
Site
ddmac.epfl.ch, la.epfl.ch

During the past few years, policy gradient methods have gained renewed attention within the control community, primarily due to their global convergence properties for certain classical control problems, such as $\mathcal{H}_2$ and $\mathcal{H}_\infty$ optimal control. However, the characteristics of policy gradient methods in the context of robust control with data-dependent uncertainty remain an open question.

This project focuses on the design and analysis of policy gradient algorithms for data-driven robust control. Given a set of noisy offline input-output data, and under assumptions on the boundedness of noise, the goal is to propose policy gradient algorithms minimizing worst-case closed-loop performance. Moreover, the properties of the proposed algorithms, such as global optimality and convergence rate, will be investigated.

Comment
Required knowledge:

1. Control theory

2. Convex optimization

3. Numerical analysis

References:

[1] Maryam Fazel, et al. “Global convergence of policy gradient methods for the linear quadratic regulator.” International conference on machine learning. PMLR, 2018.

[2] Kaiqing Zhang, Bin Hu, and Tamer Basar. “Policy Optimization for $\mathcal{H}_2$ Linear Control with $\mathcal{H}_\infty$ Robustness Guarantee: Implicit Regularization and Global Convergence.” Learning for Dynamics and Control. PMLR, 2020.

[3] Yang Zheng, Chih-fan Pai, and Yujie Tang. “Benign nonconvex landscapes in optimal and robust control, Part I: Global optimality.” arXiv preprint arXiv:2312.15332 (2023).

Professor(s)
Alireza Karimi, Zhaoming Qin
Administration
Barbara Marie-Louise Frédérique Schenkel