Highlights from IEEE CDC 2024 — Part 2: The Best Talk of the Conference

One of the things I appreciate most about conferences like the IEEE Conference on Decision and Control is their approach to presenting research. Every presentation starts with a peer-reviewed paper submission; if accepted, the work earns a spot in the program. That gives researchers at every career stage — regardless of status, age, or experience — a chance to share their ideas. Each April I'm invited to review CDC submissions, and I make it a priority to give thorough, constructive reviews. It's a level playing field, which I find refreshing compared with fields such as neuroscience, where most presentations are invitation-only plenaries and the rest are relegated to poster sessions.

Each day opened with an hour-long plenary, followed by three sessions of six 20-minute talks. With 20 parallel sessions, an attendee can catch at most ~5% of the talks, so you have to plan carefully. Among everything I managed to see, one talk stood far above the rest — even above the plenaries: "Control-Coherent Koopman Modeling: A Physical Modeling Approach," by Prof. Harry Asada (MIT). Given how technical the topic is, let me try to explain why I think this work is ground-breaking and why more control engineers should know about it.

First, what is a Koopman operator? The idea goes back to Bernard Koopman and John von Neumann (1930–31), who proved that every nonlinear system can be transformed into an infinite-dimensional linear system — in more technical terms, mapped into a linear Hilbert space. The theorems, however, aren't constructive: they don't tell you how to obtain that infinite-dimensional system, and even if you could, you'd still need to approximate it with a finite-dimensional linear system to work with it. Finding that finite-dimensional approximation has been the subject of intense work for decades — if you've heard of Dynamic Mode Decomposition (DMD), that's one such method. This is what "Koopman modeling" in the title refers to.

But to control a system you need an input — and here lies the biggest shortcoming of current methods, and what makes Prof. Asada's work so ground-breaking. So far these methods have focused on systems with no inputs (in control terms, autonomous systems). Asada's work considers systems with inputs (non-autonomous systems) and provides a way to approximate a nonlinear system, including its relationship with the input, by a finite-dimensional linear system. Consider what that means: if you can find the Koopman model of a non-autonomous nonlinear system, the control problem becomes a linear control problem, no matter how nonlinear the original system was. He showed examples, including a highly nonlinear hydraulic system whose control problem became linear under this method. If you have even a cursory knowledge of nonlinear control, you can see why I found this so exciting.

While listening, an idea struck me. Researchers analyzing neuroscience data are often already familiar with DMD for signals such as EEG or electrophysiological recordings from Utah arrays — but, because of the limitation above, these approaches typically ignore the inputs to the system, inputs that here could be the stimuli a human or animal receives while interacting with the environment. One workaround I've used myself is to apply DMD to signals from different experimental conditions and compare the extracted modes. But what if we could incorporate inputs — such as visual stimuli — into the Koopman model more explicitly? In one tempting example: what if the subject is a human driver under critical scenarios? Could we gain new insight by building a Koopman model that treats visual stimuli as inputs and EEG signals as system states — and explore the relationship between those brain states and muscle movements such as steering or braking? These are still rough ideas, but theoretical breakthroughs like this make them worth investigating.

I had a very nice chat with Prof. Asada afterward and was pleasantly surprised to learn he's been extending the concept to human locomotion. He didn't go into detail but said the work would be published soon; I'm eager to see how they apply this framework to such an interesting problem.

If you'd like to know more, I recommend their preprint on arXiv.

Part 2 of 3 — originally published on LinkedIn, January 8, 2025.