This is the website for the UCSB course ME 225FB “Nonlinear Networks: Dynamics, Learning and Applications”, Spring 2022. This website's URL is http://motion.me.ucsb.edu/ME225FB-Spring2022. A pdf version of this documentation is available on the course website.

2022 Course Description

The course is intended for graduate students interested in robust stability analysis of nonlinear networked dynamical systems. The main focus will be on contraction theory, including classic and recent developments. Secondary topics include dissipative systems theory, network small gain theory, and computational control design strategies based upon machine learning strategies.

Specific topics may include:

• a brief review of linear 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),

• logarithmic norms and linear contraction theory,

• contraction theory for nonlinear and monotone dynamical systems

  • iss, entrainment, unmodeled dynamics, equilibrium contraction, network theorems, etc

• nonlinear network systems from science and engineering, including population dynamics, coupled oscillators, traffic models, epidemic propagation models, etc

• control design via control contraction matrices and neural contraction metrics

• if time allows, theory of monotone operators (from continuous to discrete time)

Prerequisites

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

Lecture Time and Place

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

The course will be in person in room ENGR2 2243, but I may also broadcast some of the lectures on Zoom (look for an email from me with the zoom room number, otherwise please email me) and, when appropriate, share them on gauchospace/private youtube.

UCSB rules about dual-mode instruction for Spring 2022: not allowed

Course credit

Units: 3. Letter grade.

Textbook

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 I will make available.

Instructor

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: Tuesdays 4-5pm

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”

Copyright notice

My lectures and course materials, including presentations, tests, outlines, and similar materials, are protected by U.S. copyright law and by University policy. I am the exclusive owner of the copyright in those materials I create. You may take notes and make copies of course materials for your own use. You may also share those materials with another student who is enrolled in or auditing this course.

You may not reproduce, distribute or display (post/upload) lecture notes or recordings or course materials in any other way — whether or not a fee is charged — without my express prior written consent. You also may not allow others to do so. If you do so, you may be subject to student conduct proceedings under the UC Santa Barbara Student Code of Conduct.

Similarly, you own the copyright in your original papers and exam essays. If I am interested in posting your answers or papers on the course web site, I will ask for your written permission.

Resources for Students

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Help during exams

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Managing stress

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Responsible scholarship

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Furthermore, for general academic support, we encourage students to visit Campus Learning Assistance Services (CLAS) early and often. CLAS offers instructional groups, drop-in tutoring, writing and ESL services, skills workshops and one-on-one consultations. CLAS is located on the third floor of the Student Resource Building, or visit http://clas.sa.ucsb.edu.

Mental Health Statement

Students may feel overwhelmed or depressed with coursework, stress and/or other personal challenges. If you find yourself, or another student, in need of support, please do not hesitate to reach out to Counseling and Psychological Services (CAPS), 24/7 at (805) 893-4411. http://caps.sa.ucsb.edu

Gender and Sex Discrimination Policy and Student Support

Under Title IX, university students are protected from harassment and discrimination based on gender and sex. If a student feels uncomfortable or in need of support at any time related to their gender, sex, and/or sexual orientation, please contact your TA and/or course instructor immediately. If a student would like to disclose information related to pronouns, name changes, or identities, we encourage you to do so. UCSB's Resource Center for Sexual and Gender Diversity on the 3rd floor of the Student Resource Building is also available to advocate and be of and support to students.

Financial Crisis Response Team

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2020 Course Description (kept here as comparison and for further information)

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.