# Matthieu Barreau

## Hiring

No open position at the moment.

I am always looking for passionate and talented MSc students for internships or master thesis. Please contact me directly.

# Presentation

I am an Assistant Professor within the division of Decision and Control Systems at KTH, Stockholm, Sweden from September 2023.

I was an algorithm developer/research manager at Tobii and previously a postdoc with Karl Henrik Johansson at KTH. I completed my Ph.D. degree under the supervision of Alexandre Seuret and Frederic Gouaisbaut in LAAS, Toulouse, France.

On this website, you can find a list of my publications with the Matlab/Python/Julia code used for them (if I took the time to upload it correctly on GitHub). For more information feel free to contact me.

# Research profile

Optimization of performances and stability analysis of heterogeneous dynamical systems are at the core of my research activities. It translates into an optimization problem under constraints such as model dynamics, stability, saturation, sampling, or delayed control. I actively participate in theory developments and applications in this field.

I am interested in both finding the exact solution to the aforementioned optimization problem, using relaxations to get a semidefinite program, and approximating a solution using machine learning techniques. I then use tools from robust control such as Lyapunov functions and Integral Quadratic Constraints (IQCs) in combination with Physics-Informed Neural Networks (PINNs - see the video on the right). The latter are traditional feedforward neural networks whose output has been enriched by its derivatives with respect to its inputs. This consequently leads to a learning problem under the constraint that the differential equation must hold.

My research expertise and interest are described in the figure above. They consist of three steps and their relations between them. It can be summarized as follows.

What can I expect from my data?

Depending on the sparsity in the measurements, the quality of the signals, and the fidelity of the model, one can decide on the problem type. In the more restrictive case, one can simulate the system and infer its state relatively far from measurements, this is a digital twin framework. In case of more data, one can start estimating uncertain parameters in the model or propose a richer dynamic. Long-term inference can also be made possible.How can I train a PINN?

Training a PINN is like solving a learning problem under constraint. There are then different methodologies coming from constrained optimization, mainly Lagrangian relaxations. This choice is highly correlated to the type of problem discussed previously and the limited training time. The architecture of the neural network also reflects the a-priori knowledge of the system and affects the computational/memory burden.Which tool do I need to attain the desired level of certification?

Finally, the last step is to evaluate the quality of the training. The general approach tends to consider the inherent stochasticity of the training process and gives confidence intervals on the inference. A more formal approach evaluates the solution using IQCs to ensure that the signal has the desired level of performance. Once the PINN is trained, this can also be used as an initial guess to standard algorithms already certified. This last step can also be tackled first depending on the problem.

These three questions shape the methodology that I will apply in the research program described below. My research is focusing on re-interpretation and coupling between system theory and machine learning. This is conducted in an international environment, mainly with researchers from all over Europe and the US.

# Research interests

Physics informed neural networks; traffic systems;

Time-Delay Systems; Infinite dimensional systems;

Lyapunov Methods; Integral Quadratic Constraints;.

Research Gate - Google Scholar - GitHub

# Highlights

8th of May: Relase of the tf2-bfgs package

3rd May 2024: New PhD opening

1 September 2023: I am now an Assistant Professor at KTH

30 March 2023: I wrote a tutorial for CDC 2022 entitled "New Frontiers of Freeway Traffic Control and Estimation".

24 May 2022: I was a plenary speaker during a SAGIP workshop about tackling the infinite dimension in control problems.

22 April 2021: I gave a general talk at Digital Future about Physics-informed learning. The video is uploaded on YouTube