Syllabus for “Nonlinear Network Systems” - Francesco Bullo, UCSB ME 225FB, Spring 2022

Week #01

course logistics: description and syllabus
course topics: theory and examples
introduction to contraction theory and network systems
Chp01: log norms, basic definitions and properties

Week #02

Chp01: log norms, quadratic forms, weak pairings, spectral and monotonicity properties, efficiency

Week #03

Chp02: contraction theory: one-sided Lipschitz maps, main equivalence theorem, strong infinitesimal contraction
Chp02: properties of strongly contracting dynamics

Week #04

Chp03: Hopfield neural networks
Chp03: Lure’ models via incremental quadratic stability
Chp02: weakly contracting systems, dichotomy and sufficient conditions for stability
Chp03: distributed primal dual optimization

Week #05

Chp02: monotone dynamics: definition
monotone osL
monotone contracting systems: strong and weak contraction
Chp03: Daganzo traffic models

Decide topic for your Final Report and Final Presentation by May 1st or earlier
Students are encouraged to work in pairs.

Week #06

convex functions, gradient systems, contracting algorithms (from book exercises and Neurips paper)
Kuramoto phase-coupled oscillators (from chapter in old book + new slides)

Material for the rest of the quarter depends upon time and interest.

Week #07

Chp02 and Chp03: equilibrium contracting and Yorke SIS epidemic model
Chp02 and Chp03: semicontractivity and diffusively-coupled oscillators

Francesco out of town during part of week 8. Arrangements to be made.

Week #08

Appendix C: Networks of passive systems
diagonal stability
Networks of Dissipative Systems, from M. Arcak and C. Meissen and A. Packard, 2016

Week #09

control design via control contraction matrices
neural contraction metrics

Week #10 and Finals week

final presentations

FINAL PRESENTATIONS

Final report due on XXX at midnight, electronic format, email to FB
Final presentations: Time: to be determined, during (or right before) Final's Week
Final presentations: Place: ME Classroom, EII 2243