Control of Unknown Dynamical Systems: Robustness and Online Learning of Feedback Control

Citation

Ho, Dimitar Mi (2024) Control of Unknown Dynamical Systems: Robustness and Online Learning of Feedback Control. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/fb64-vk24. https://resolver.caltech.edu/CaltechTHESIS:09062023-095903699

Abstract

Over the past few decades, our physical and digital worlds have become increasingly intertwined and reliant on each other. Advancements in areas such as machine learning, online optimization, and control theory, along with ubiquitous access to computational power, have played a crucial role in this technological evolution. As a result, we are now moving towards a future where complex and intelligent dynamical systems, with humans in the loop, govern our daily lives.

Building advanced control systems is a critical step in this journey, as they enable swift and data-informed decision-making. However, as we aim to create even more sophisticated closed-loop systems, we must proceed with a careful balance of ambition and caution. While the benefits of these interconnected systems are abundant and our dependence on them deepens, ensuring the actual reliability and safety of the systems becomes increasingly challenging due to the growing complexity of their dynamics. This challenge is particularly prominent in safety-critical applications involving physical systems, which often have strict and non-negotiable safety and performance requirements. To establish a harmonious relationship between our physical and digital worlds, it is crucial to develop intelligent closed-loop control systems that are not only fast and efficient, but also reliable and fault-tolerant.

The title of this thesis, "Control of Unknown Dynamical Systems: Robustness and Online Learning of Feedback Control," reflects the central focus of this work on addressing this pressing challenge. The thesis aims to develop theoretical frameworks and tools that provide insights and contribute new approaches to the design of control systems capable of handling the inherent uncertainty in real-world dynamical systems.

The first part of the thesis focuses on the design of closed-loop systems that are robust to dynamic uncertainty, particularly in settings involving nonlinear dynamics and complex control constraints. The second part introduces a general framework for learning-to-control algorithms that provide worst-case guarantees, even in scenarios where the dynamic uncertainty is arbitrarily large. By addressing these key aspects, this work aims to advance our understanding and capabilities in designing control systems that can effectively deal with uncertainty.

Thesis Files