UCSB “Nonlinear Networks: Dynamics, Learning and Applications” ME 225FB, Spring 2022 Instructor: Francesco Bullo
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.
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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.
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