Seminar Details
2024-09-24 (14h) : Newcomer seminar (postdocs)
At Euler building (room a.002)
Organized by Mathematical Engineering
Section 1: Synchronization Analysis, Control and Verification of Complex Networked Systems
Speaker :
Shuyuan Zhang
Abstract :
Synchronization is a kind of common collective phenomenon in nature, which has a quite wide range of applications for various subjects, including physics, biology, control science, social science. A typical way of analyzing synchronization of complex networked systems is to establish the synchronization criteria based on quadratic Lyapunov functions. Beyond the challenge of obtaining quadratic Lyapunov functions, the serious challenge is no guarantee of Lyapunov functions of the quadratic form for some systems. However, for these systems, there may exist general Lyapunov functions. Inspired by this fact, we propose several less conservative synchronization criteria by using general Lyapunov functions beyond quadratic ones. Then, the synchronization problem is transformed into a sum-of-squares optimization problem. The resulting sum-of-squares-based optimization algorithm efficiently generates polynomial Lyapunov functions, facilitating automatic synchronization verification. The obtained results are less conservative and are applicable for more systems, not only homogeneous networked systems but also heterogeneous networked systems.
Section 2: A coarse view on dynamical systems, control and optimization
Speaker :
Wouter Jongeneel
Abstract :
It is not clear if our field would be in this state without early efforts towards understanding stability of the solar system. At that time---as explicit integration turned out to be overly complicated, the key insight was not to approximate, but to move away from the quantitative. The result was the inception of a more qualitative study of dynamical systems, with the overall philosophy being nicely captured by Conley: "... if such rough equations are to be of use it is necessary to study them in rough terms ...".
Now, flash-forward to 2024, with the advent of computational power and data storage, the focus shifted again to the quantitative. It is hard to find papers without sample complexities, probabilistic bounds and a statistical analysis of extensive simulations. This viewpoint is evidently very important towards safe and practical algorithms, for instance, regarding a control system. So is there still room for something qualitative?
In this talk we discuss open homotopy questions (and partial resolutions) in dynamical systems, topological insights in control systems and we comment on some optimization problems. With these examples we hope to show that there is indeed room---and arguably a need, for more qualitative work in a quantitative age.