Machine Learning and Optimal Control
A late-summer school for students
September 9, 10, 12:
Prof. L. Gruene - An Introduction to Optimal Control and Recent Solution Strategies
September 30, October 1:
Prof. E. Zuazua - Machine Learning: A Mathematician's Perspective
Organizers: Carlo Mariconda, Monica Motta, Giulia Treu
About the Lecture Series
This late-summer lecture series offers students in Mathematics, Engineering, and Computer Science the chance to go beyond the standard curriculum and gain insight into some of today's most active areas of research.
Over the course of five lectures, two internationally recognized scholars will present key ideas that connect optimal control theory, machine learning, and systems analysis. The aim is to provide an accessible yet rigorous introduction to concepts that play a central role in both pure and applied mathematics.
Featured Speakers
Prof. Lars Grüne
University of Bayreuth
Will discuss the foundations of optimal control, highlighting classical techniques as well as modern approaches such as model predictive control and deep reinforcement learning.
Prof. Enrique Zuazua
FAU Erlangen-Nürnberg
Will offer a mathematician's perspective on machine learning, exploring its deep links with control theory, cybernetics, and applied mathematics.
Why Attend?
These lectures are designed to be accessible to motivated students, offering a clear view of how mathematical ideas evolve and influence cutting-edge technologies. They are also a valuable opportunity to meet leading experts, ask questions, and discover possible connections to your own studies and future research interests.
Whether you are intrigued by how the mathematics you study can be applied beyond the classroom, or you are considering delving deeper into these areas for your future studies or career, this short series is designed to broaden your perspective, inspire new questions, and show you the vibrant, evolving side of mathematical research.
An Introduction to Optimal Control and Recent Solution Strategies
LARS GRUENE
https://num.math.uni-bayreuth.de/en/team/lars-gruene/
Schedule - Prof. Grüne
1
September 9 (Tuesday)
3:30 – 5:30 PM in 1C150 (Torre Archimede)
2
September 10 (Wednesday)
3:30 – 5:30 PM in 1C150 (Torre Archimede)
3
September 12 (Friday)
10:30 – 12:30 AM in 1C150 (Torre Archimede)
Course Abstract & Schedule
Abstract: In this course I provide an introduction to optimal control theory and related computational methods. The course starts with definitions and examples for optimal control problems. I will then explain the mathematical background of the most common solution methods and their numerical implementation. A particular focus will be on optimal feedback control, which I will motivate by real-world and academic applications. For computing optimal feedback laws, I will present two of the currently most widely used solution methods, which are model predictive control and deep reinforcement learning. For these, I will also explain some of the mathematical background and open questions.
Tentative schedule:
Session 1
Definitions and examples of optimal control problems, Solution methods
Session 2
Solution methods and their numerical implementation
Session 3
Model predictive control and deep reinforcement learning
About Prof. Lars Grüne
Lars Grüne has been Professor for Applied Mathematics at the University of Bayreuth, Germany, since 2002. He received his Diploma and Ph.D. in Mathematics in 1994 and 1996, respectively, from the University of Augsburg and his habilitation from the J.W. Goethe University in Frankfurt/M in 2001. He held or holds visiting positions at the Universities of Rome Sapienza (Italy), Padova (Italy), Melbourne (Australia), Paris IX – Dauphine (France), Newcastle (Australia) and IIT Bombay (India). Prof. Grüne was General Chair of the 25th International Symposium on Mathematical Theory on Networks and Systems (MTNS 2022), he is Editor-in-Chief of the journal Mathematics of Control, Signals and Systems (MCSS) and is or was Associate Editor of various other journals, including the Journal of Optimization Theory and Applications (JOTA), Mathematical Control and Related Fields (MCRF) and the IEEE Control Systems Letters (CSS-L). His research interests lie in the area of mathematical systems and control theory with a focus on numerical and optimization-based methods for nonlinear systems.
Machine Learning: A Mathematician's Perspective
Enrique ZUAZUA
1
September 30 (Tuesday)
12:30 - 2:30 PM in 1C150 (time and room to be confirmed)
2
October 1 (Wednesday)
4:30 - 6:30 PM in 1C150 (time and room to be confirmed)
https://dcn.nat.fau.eu/enrique-zuazua/
Course Description
Machine Learning has emerged as one of the most transformative forces in science and technology. Beneath its powerful algorithms lie mathematical foundations deeply rooted in classical disciplines such as Applied Mathematics and Systems Control. This lecture series adopts a mathematician's perspective to examine why Machine Learning works so effectively and how its data-driven paradigms can be rigorously integrated into traditional analytical frameworks.
We will revisit the historical and conceptual links between Machine Learning and Systems Control—also known as Cybernetics—a field shaped by the pioneering ideas of Ampère and Wiener. Their parallel evolution reveals a deep mathematical unity and highlights the power of mathematics to model complex systems and drive innovation.
This dual perspective is mutually enriching. On one hand, Machine Learning raises fundamental mathematical questions that challenge and inspire the mathematical community. On the other, it offers opportunities to expand the scope of classical applied mathematics by developing hybrid methodologies that integrate data-driven insights.
The series will conclude by outlining promising directions for future research at the intersection of Machine Learning, Applied Mathematics, and Control Theory.
About Prof. Enrique Zuazua
Enrique Zuazua (Eibar, Basque Country – Spain, https://dcn.nat.fau.eu/zuazua) holds, since September 2019, the Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at the Department of Mathematics of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) in Germany and part-time appointments at Universidad Autónoma de Madrid (UAM) and Fundación Deusto, Bilbao. He is also a member of the Basque Academy "Jakiunde", Fellow of the Artificial Intelligence Industry Academy (AIIA) and of the Academia of Europaea, and cooperates with the artificial intelligence company Sherpa AI in Bilbao and with SHARE-Schaeffler in Erlangen.