This course (6 ECTS) offers a foundational exploration of leveraging machine learning techniques for dynamical systems. Students will gain essential insights into dynamical system theory, learning how to model and control systems based on observed data. Key topics in dynamical systems encompass the representation of nonlinear systems, stability analysis, fundamental control concepts, and identification methods. The course delves into various machine learning approaches, emphasizing supervised learning techniques with a specific focus on data-driven system identification, Bayesian approaches and physics-informed learning. Practical applications of these methodologies are highlighted through examples predominantly centered around mechanical and robotic systems.

By the end of the course, students will possess a solid understanding of the symbiotic relationship between machine learning and dynamical systems, enabling them to apply these concepts in real-world scenarios.

After completing the course, the students will

• understand fundamental concepts of linear and nonlinear dynamical systems.

• know commonly used machine learning techniques for the modeling and identification of dynamical systems.

• know how to benefit from data-driven approaches for feedback control and model predictive control approaches.

• understand the benefits of applying probabilistic and physics-informed learning to dynamical systems.

Basic knowledge of linear algebra, probability theory, multivariate calculus and concepts of machine learning. No knowledge in control theory required.

Primary textbook:

• Brunton, Steven L., and J. Nathan Kutz. Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2022. 

Secondary textbooks:

• Isidori, Alberto, ed. Nonlinear control systems: an introduction. London : Springer London : Imprint: Springer, 1995. 

• Kocijan, Juš. Modelling and control of dynamic systems using Gaussian process models. Cham: Springer International Publishing, 2016. 

• Karniadakis, George Em, et al. “Physics-informed machine learning.” Nature Reviews Physics 3.6 (2021): 422-440. 

• Kouvaritakis, Basil, and Mark Cannon. “Model predictive control.” Switzerland: Springer International Publishing 38 (2016). 

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