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Learning and Control of Dynamical Systems


Lale, Ali Sahin (2023) Learning and Control of Dynamical Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rdhq-8a88.


Despite the remarkable success of machine learning in various domains in recent years, our understanding of its fundamental limitations remains incomplete. This knowledge gap poses a grand challenge when deploying machine learning methods in critical decision-making tasks, where incorrect decisions can have catastrophic consequences. To effectively utilize these learning-based methods in such contexts, it is crucial to explicitly characterize their performance. Over the years, significant research efforts have been dedicated to learning and control of dynamical systems where the underlying dynamics are unknown or only partially known a priori, and must be inferred from collected data. However, much of these classical results have focused on asymptotic guarantees, providing limited insights into the amount of data required to achieve desired control performance while satisfying operational constraints such as safety and stability, especially in the presence of statistical noise.

In this thesis, we study the statistical complexity of learning and control of unknown dynamical systems. By utilizing recent advances in statistical learning theory, high-dimensional statistics, and control theoretic tools, we aim to establish a fundamental understanding of the number of samples required to achieve desired (i) accuracy in learning the unknown dynamics, (ii) performance in the control of the underlying system, and (iii) satisfaction of the operational constraints such as safety and stability. We provide finite-sample guarantees for these objectives and propose efficient learning and control algorithms that achieve the desired performance at these statistical limits in various dynamical systems. Our investigation covers a broad range of dynamical systems, starting from fully observable linear dynamical systems to partially observable linear dynamical systems, and ultimately, nonlinear systems.

We deploy our learning and control algorithms in various adaptive control tasks in real-world control systems and demonstrate their strong empirical performance along with their learning, robustness, and stability guarantees. In particular, we implement one of our proposed methods, Fourier Adaptive Learning and Control (FALCON), on an experimental aerodynamic testbed under extreme turbulent flow dynamics in a wind tunnel. The results show that FALCON achieves state-of-the-art stabilization performance and consistently outperforms conventional and other learning-based methods by at least 37%, despite using 8 times less data. The superior performance of FALCON arises from its physically and theoretically accurate modeling of the underlying nonlinear turbulent dynamics, which yields rigorous finite-sample learning and performance guarantees. These findings underscore the importance of characterizing the statistical complexity of learning and control of unknown dynamical systems.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Reinforcement Learning, Machine Learning, Control, Adaptive Control, Regret Minimization, System Identification, Nonlinear Systems
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Anandkumar, Anima
Thesis Committee:
  • Vaidyanathan, P. P. (chair)
  • Abu-Mostafa, Yaser S.
  • Anandkumar, Anima
  • Hassibi, Babak
  • Wierman, Adam C.
Defense Date:5 May 2023
Non-Caltech Author Email:sahinlale93 (AT)
Record Number:CaltechTHESIS:05282023-011333603
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 2 adapted for ch. 3 adapted for ch. 3 adapted for ch. 4 adapted for ch. 4 adapted for ch. 5 adapted for ch. 5 adapted for ch. 5 adapted for ch. 5 adapted for ch. 6 adapted for ch. 6
Lale, Ali Sahin0000-0002-7191-346X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15219
Deposited By: Ali Sahin Lale
Deposited On:05 Jun 2023 20:47
Last Modified:13 Jun 2023 18:41

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