Polynomial Sum-of-Squares - Data-Driven Dynamics | Lecture 13

Verifying nonnegativity of a polynomial turns out to be a hard task. One way of making it easier is to verify it admits a representation as a sum of square (SOS) polynomials. In this lecture we explain the basics of SOS methods for verifying nonnegativity of polynomials and how it can be applied to identifying Lyapunov function. The method is computational and frames identifying polynomial SOS functions as a semidefinite program that can be solved using interior point methods. We provide an example of identifying a (numerical) Lyapunov function for a planar ordinary differential equation. Learn more about polynomial SOS and optimization: https://en.wikipedia.org/wiki/Sum-of-squares_optimization Coding demonstration in MATLAB comes from MG_LyapFn.m here: https://github.com/jbramburger/DataDrivenDynSyst/tree/main/Data-Driven%20Polynomial%20Optimization Download YALMIP here: https://yalmip.github.io/download/ Download MOSEK here: https://www.mosek.com/downloads/ Get the book here: https://epubs.siam.org/doi/10.1137/1.9781611978162 Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDrivenDynSyst This book provides readers with: - methods not found in other texts as well as novel ones developed just for this book; - an example-driven presentation that provides background material and descriptions of methods without getting bogged down in technicalities; - examples that demonstrate the applicability of a method and introduce the features and drawbacks of their application; and - a code repository in the online supplementary material that can be used to reproduce every example and that can be repurposed to fit a variety of applications not found in the book. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.