Focus Period Linköping 2023
PhD Course – Theory and Applications of Contracting Dynamical Systems
Francesco Bullo, Mechanical Engineering, UC Santa Barbara
Theory and Applications of Contracting Dynamical Systems
Over the last two decades, engineers and mathematicians have made remarkable progress on the application of the Banach contraction principle to dynamical systems over networks. The basic contraction property is now understood for discrete and continuous time systems, with respect to Euclidean and non-Euclidean norms, in closed and open systems, and for single agents and networks of systems. In this set of lectures, I will present this theoretical field and its applications. Topics will include (i) the algebraic properties of the induced norms and logarithmic norms of matrices, (ii) contracting dynamics over finite-dimensional vector spaces endowed with Euclidean and non-Euclidean norms, and (iii) weakly-contracting dynamics and monotone dynamics. Numerous examples will be presented, including Hopfield neural networks, interconnected contracting systems, and gradient and primal/dual flows of convex functions.
The reference text for the course is the recent text “Contraction Theory for Dynamical Systems”, KDP, v1.1, 2023, ISBN 979-8836646806, freely available at: https://fbullo.github.io/ctds/.
Where: ISY Linkoping University
Time: Wed, Th, Fri September 13,14,15.
Duration: 4h/day (total 12h)
It will be possible to take the course for credits. Info on the format of the exam and n. of credits (likely 3 credits) will be added later on.
Send an email to C. Altafini at email@example.com.