UCSB “Nonlinear Systems: Dynamics, Learning and Applications”
ME 225FB, Fall 2020
Instructor: Francesco Bullo

This is the website for the UCSB course ME 225FB “Nonlinear Networks: Dynamics, Learning and Applications”, Fall 2020. This website's URL is http://motion.me.ucsb.edu/ME225FB-Fall2020. A pdf version of this documentation is available on the course website.

Course Description

The course is intended primarily for graduate students interested in nonlinear dynamical systems, learning methods for dynamical systems, and applications. Roughly one third of the course will focus on nonlinear network analysis theories such as contraction theory, dissipative systems and network small gain theory. A second third will focus on example systems from robotics, industrial control systems, traffic systems, mathematical sociology, and power grids. Finally, the course will review kernel-based methods in learning dynamical systems.

2018 Course Description (kept here as comparison and for further information)

The course is intended primarily for graduate students interested in nonlinear dynamical systems and nonlinear control systems as arising in cooperative control, distributed algorithms, distributed systems, and network science. Topics will include:

  • a brief review of network systems theory (as in ME269) and of Lyapunov and LaSalle stability theory (as in ME236), as applied to network dynamical systems (averaging, compartmental systems),

  • passivity theory

  • network small gain theory

  • theory of competitive/cooperative and monotone systems,

  • contraction theory (applied to network and diffusively coupled systems)

  • example applications from robotics, industrial control systems, traffic systems, mathematical sociology, and power grids.


Competency in linear algebra, nonlinear dynamical systems and linear control systems.

Lecture Time and Place

The course will be on Zoom. Zoom room to be announced via email.

Tue and Thu: 9:30am-10:45am (as on GOLD and egrades)

Course credit

Units: 3. Letter grade.


All linear background is available at: http://motion.me.ucsb.edu/book-lns

For the nonlinear treatment, the first and second part of the course are still incomplete, but covered in part of a set of lecture notes, entitled “Lecture on Nonlinear Network Systems” that will be available on GauchoSpace.

For the learning dynamics topic, I will provide PDFs of recent articles.


Professor Francesco Bullo
Department of Mechanical Engineering
Email: bullo-at-engineering.ucsb.edu
Website: http://motion.me.ucsb.edu

Office hours = Discussion times

Place: zoom. Time: To be determined

Grading for ME 225FB

The class grade is based on a final written report and a final oral presentation. Read more about it in the PDFs entitled “Instructions for Final Presentations and Reports”

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