Uploaded October 2022 | Updated September 2026, 2 weeks ago
This video investigates a 2-dimensional linear system of ordinary differential equations with a pair of purely imaginary complex conjugate eigenvalues. These solutions are known as neutrally stable center fixed points. We investigate the solutions using eigenvalues and eigenvectors, as well as with phase portrait pictures.
Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview
3:09 Examples of physical systems with complex eigenvalues
5:12 Quick recap of basic properties of complex numbers
9:50 Computing the eigenvectors
16:34 Writing the full solution
25:04 Geometric intuition: The solution is a rotation matrix
31:15 Adding small friction: Center becomes spiral sink
This video investigates a 2-dimensional linear system of ordinary differential equations with a pair of purely imaginary complex conjugate eigenvalues. These solutions are known as neutrally stable center fixed points. We investigate the solutions using eigenvalues and eigenvectors, as well as with phase portrait pictures.
Playlist: youtube.com/playlist?list=PLMrJAkhIeNNTYaOnVI3QpH7jgULnAmvPA
Course Website: http://faculty.washington.edu/sbrunton/me564/
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Overview
3:09 Examples of physical systems with complex eigenvalues
5:12 Quick recap of basic properties of complex numbers
9:50 Computing the eigenvectors
16:34 Writing the full solution
25:04 Geometric intuition: The solution is a rotation matrix
31:15 Adding small friction: Center becomes spiral sink
![[1/8] Control for Societal-Scale Challenges: Road Map 2030 [Introduction]](https://i.ytimg.com/vi/btWyzKmU9wM/mqdefault.jpg "[1/8] Control for Societal-Scale Challenges: Road Map 2030 [Introduction]
This video provides a high level introduction for this new road map document outlining some of the biggest societal challenges we face, and how control theory will be central in helping address them.
https://www.ieeecss.org/control-societal-scale-challenges-road-map-2030
The production of this video was supported by the IFAC.
Roadmap Abstract: The world faces some of its greatest challenges of modern time and how we address them will have a dramatic impact on the life for generations to come. Simultaneously, control systems, consisting of information enriched by various degrees of analytics followed by decision-making, are pervading a variety of sectors, not only in engineering but beyond, into financial services, socio-economic analysis, entertainment and sports, and political and social sciences. Increased levels of automation are sought after in various sectors and being introduced into new domains. All of these advances and transformations urge a shift in the conversation toward how control systems can meet grand societal- scale challenges. The document seeks to chart a roadmap for the evolution of control systems, identifying several areas where our discipline can have an impact over the next decade.
Edited by: Anuradha M. Annaswamy, Karl H. Johansson, and George J. Pappas
Authors: Andrew Alleyne, Frank Allgöwer, Aaron D. Ames, Saurabh Amin, James Anderson, Anuradha M. Annaswamy, Panos J. Antsaklis, Neda Bagheri, Hamsa Balakrishnan, Bassam Bamieh, John Baras, Margret Bauer, Alexandre Bayen, Paul Bogdan, Steven L. Brunton, Francesco Bullo, Etienne Burdet, Joel Burdick, Laurent Burlion, Carlos Canudas de Wit, Ming Cao, Christos G. Cassandras, Aranya Chakrabortty, Giacomo Como, Marie Csete, Fabrizio Dabbene, Munther Dahleh, Amritam Das, Eyal Dassau, Claudio De Persis, Mario di Bernardo, Stefano Di Cairano, Dimos V. Dimarogonas, Florian Dörfler, John C. Doyle, Francis J. Doyle III, Anca Dragan, Magnus Egerstedt, Johan Eker, Sarah Fay, Dimitar Filev, Angela Fontan, Elisa Franco, Masayuki Fujita, Mario Garcia-Sanz, Dennice Gayme, Wilhelmus P.M.H. Heemels, João P. Hespanha, Sandra Hirche, Anette Hosoi, Jonathan P. How, Gabriela Hug, Marija Ilić, Hideaki Ishii, Ali Jadbabaie, Matin Jafarian, Samuel Qing-Shan Jia, Tor Arne Johansen, Karl H. Johansson, Dalton Jones, Mustafa Khammash, Pramod Khargonekar, Mykel J. Kochenderfer, Andreas Krause, Anthony Kuh, Dana Kulić, Françoise Lamnabhi-Lagarrigue, Naomi E. Leonard, Frederick Leve, Na Li, Steven Low, John Lygeros, Iven Mareels, Sonia Martinez, Nikolai Matni, Tommaso Menara, Katja Mombaur, Kevin Moore, Richard Murray, Toru Namerikawa, Angelia Nedich, Sandeep Neema, Mariana Netto, Timothy O’Leary, Marcia K. O’Malley, Lucy Y. Pao, Antonis Papachristodoulou, George J. Pappas, Philip E. Paré, Thomas Parisini, Fabio Pasqualetti, Marco Pavone, Akshay Rajhans, Gireeja Ranade, Anders Rantzer, Lillian Ratliff, J. Anthony Rossiter, Dorsa Sadigh, Tariq Samad, Henrik Sandberg, Sri Sarma, Luca Schenato, Jacquelien Scherpen, Angela Schoellig, Rodolphe Sepulchre, Jeff Shamma, Robert Shorten, Bruno Sinopoli, Koushil Sreenath, Jakob Stoustrup, Jing Sun, Paulo Tabuada, Emma Tegling, Dawn Tilbury, Claire J. Tomlin, Jana Tumova, Kevin Wise, Dan Work, Junaid Zafar, Melanie Zeilinger
This video was produced at the University of Washington")
![Python Symbolic Regression (PySR) [Physics Informed Machine Learning]](https://i.ytimg.com/vi/df43V4OjMVs/mqdefault.jpg "Python Symbolic Regression (PySR) [Physics Informed Machine Learning]
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
02:14 What is Symbolic Regression?
04:08 High-Level Algorithm/ Genetic Programming Overview
// 05:26 Crossover and Mutation
08:12 History of Symbolic Discovery/ Background: Symbolic Discovery
// 09:16 Symbolic Discovery Case Study
// 11:15 Case Study: Control Laws
12:18 Why PySR
// 12:18 PySR: Features
// 13:15 PySR: Benchmarks
// 14:00 PySR: Code Structure
14:19 Why Symbolic Regression/ Potential Outro
15:48 Outro")
