Data-driven design for complex dynamic systems
Chris Verhoek defended his PhD thesis with the distinction cum laude at the Department of Electrical Engineering on May 13th.
A new way to approach complex systems
To control nonlinear systems effectively, it鈥檚 essential to understand their behavior across a wide range of conditions. Instead of working with traditional models, this research of Verhoek starts with raw system data鈥攊nput and output measurements鈥攁nd builds controllers from there.
The key idea is to reformulate system behavior using what鈥檚 called velocity dynamics. Rather than focusing on the system鈥檚 state at a given time, this approach looks at how those states change. This shift makes the system easier to analyze and control without tying it to a specific operating point.
These velocity dynamics can then be represented in a structure known as Linear Parameter-Varying (LPV) form. LPV systems bridge the gap between simple linear models and more complex nonlinear ones, offering a flexible way to design reliable controllers.
Building controllers directly from data
A major innovation in this work is the extension of a foundational tool in data-driven control鈥攖he Fundamental Lemma鈥攖o LPV systems. This breakthrough makes it possible to construct accurate system representations using only measured data, bypassing the modeling step entirely.
With this data-driven LPV representation, the research develops methods to analyze system stability and energy efficiency. It also enables the design of various controller types, including predictive controllers that anticipate future behavior.
These controllers come with strong theoretical guarantees: they can ensure that the system remains stable and performs well under a wide range of conditions, even in the presence of complex nonlinear behavior.
Tested and proven in practice
The methods developed were tested in academic settings, simulations, and real-world experiments. They consistently matched or exceeded the performance of traditional, model-based controllers. In particular, they significantly outperformed existing data-driven methods that can only handle simplified, linear systems.
This demonstrates that high-performance control from data is not just a theoretical possibility鈥攊t works in practice, even for highly complex systems.
A fundamental step forward
This research delivers more than just new algorithms. It introduces a new way of thinking about control design鈥攐ne that eliminates the need for detailed, often infeasible modeling processes.
By allowing high-performance controllers to be built directly from data, this framework makes it possible to manage the complexity of systems that power our energy infrastructure, improve our electronics, and expand our scientific capabilities. And it does so with rigorous guarantees for both safety and performance.
In short, this work lays the foundation for a new generation of intelligent, efficient, and reliable systems鈥攄riven not by models, but by the data they generate.
Title of PhD thesis: . Supervisors: Prof. Roland Toth, and Dr. Sofie Haesaert.
PhD in the picture
What was the most significant finding from your research, and what aspects turned out to be most important to you?
I find it difficult to pinpoint which result is the most significant. I think of my work as a framework, a realization of vision. This realization, so the development of our framework, is the significant finding. The fact that my research encompasses the development of a novel framework is also the thing I am most proud of. What I really like about my research trajectory, is that some aspects that I developed during my MSc thesis actually came back at the end of my PhD.
What was your motivation to work on this research project?
I wanted to do some fundamental work. I first studied HBO Mechatronics, which is really practically focused, and the question of why things work the way they work is鈥� less important. This is often not a problem, in fact, I believe that right now we need significantly more do-ers than thinkers. But my love for mathematics and difficult problems made me part of the latter team. When my promotor, Roland T贸th, came with this project on the question of 鈥渉ow can we design controllers with guarantees without knowing the model?鈥�, I was sold.
What was the greatest obstacle that you met on the PhD journey?
I really enjoyed my PhD, so I have to think hard of obstacles. There is the occasional imposter syndrome or insecurity when you get a negative review from an article, but generally I had a positive experience. Maybe the biggest obstacle was a jumpscare during the writing of my thesis, where I found a bug in my code that broke a simulation. This simulation actually demonstrated a fundamental result in my thesis. Luckily, I just coded it very inefficiently and a colleague who is better in Matlab than me showed how to correctly and efficiently implement the problem. With this new implementation it worked like a charm.
What did you learn about yourself during your PhD research journey? Did you develop additional new skills over the course of the PhD research?
I learned that I really enjoy the 鈥榓cademic game鈥�, the politics, the networking, etc. I learned that being a researcher is so much more than just research. For example, selling your work is very important, but at the same time very subtle. As a Dutch person, you鈥檙e raised to be modest about your capabilities and not stand out of line too much (doe maar normaal, dan doe je al gek genoeg). However, with this mentality in research, especially on a global scale, you will not be recognised. No one will sell your work, apart from yourself. So, if you want to make impact, then you better sell it (but definitely not oversell, which is where this subtlety is). Finding this balance is definitely a skill that I started to develop over the years, although I鈥檓 still learning.
What are your plans for after your PhD research?
My plan is to stay in academia, and hopefully in the future be a professor at a Dutch university (preferably 色中色, of course). On short terms, I will complete some of the unfinished articles from my PhD in the upcoming few months. If everything goes well, I will start a postdoctoral research position in the US at the end of 2025.