PhD defense - Peter Coppens

Provable Safe Learning-based Control of Uncertain Systems

Start: 13/05/2024, 17:00
Location: aula van de Tweede Hoofdwet

Abstract

This project investigates the design of controllers for dynamic systems. These are systems whose state evolves over time. Examples, include cars, drones, power distribution networks, biochemical reactions, etc. When controlling such systems, it is essential to predict future behavior. In many applications, these predictions can be made using models based on physics. However, in some cases, these models are not available due to the inherent complexity of the system. Examples include human interactions crucial in self-driving cars, aerodynamic effects on drones flying close to objects, etc. If a model cannot be used, uncertainty arises that we must actively mitigate by learning about the environment based on examples of past behavior. Our goal is then to exploit this learned behavior in a controller.

To learn safely, we employ a three-step procedure. We start by using data to estimate a distribution of future trajectories. Then we evaluate the errors in this distribution due to the limited amount of available data. Finally, we ensure that our controller performs well under all possible errors. To predict these errors, we leverage existing fundamental results from the statistical literature. We also extend these by examining how data sorting can be used to estimate errors. This also has independent applications in areas such as machine learning, where it allows for more learning from the same amount of data. To make the controller robust against distributional errors, we use distributionally robust optimization. We describe a flexible and rigorous framework to computationally solve the resulting problems.

These tools are then applied to a broad, abstract class of dynamics where we can guarantee that the learning controller will meet certain conditions. Specifically, we demonstrate that the controller is stable, and thus, the state will converge to a specific value. We can also design controllers that constrain the state to a particular region. We describe how the controller becomes more cautious as more data becomes available, until we can make nearly perfect predictions and exploit them optimally. We also provide an upper bound on a quantitative measure of performance. Since we are working with statistical models, there is always a small probability that the data is not representative of the system's behavior, invalidating the aforementioned guarantees. Therefore, we also provide a quantitative prediction of this probability.

The entire framework serves as a bridge between system identification and optimal control, giving it a unique position in the literature. In the project, we also describe various challenges in establishing this bridge, which open up further research directions. One of the most crucial aspects in estimating errors in statistical learning techniques. Therefore, we offer concrete suggestions on how existing methods can be improved in the future.

URL: https://www.kuleuven.be/doctoraatsverdediging/fiches/3E19/3E190564.htm