Uploaded November 2022 | Updated September 2026, 1 week ago
This video explores a central result in dynamical systems: The Hartman-Grobman theorem. This theorem establishes when a fixed point of a nonlinear system will resemble its linearization. In particular, hyperbolic fixed points, where every eigenvalue has a non-zero real part, will be "structurally stable" so that the nonlinear system resembles its linearization in a neighborhood of the fixed point. We also discuss the existence of stable and unstable manifolds.
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 Hartman-Grobman and hyperbolic fixed points
10:36 Stable and unstable manifolds
13:50 Example of stable manifold
This video explores a central result in dynamical systems: The Hartman-Grobman theorem. This theorem establishes when a fixed point of a nonlinear system will resemble its linearization. In particular, hyperbolic fixed points, where every eigenvalue has a non-zero real part, will be "structurally stable" so that the nonlinear system resembles its linearization in a neighborhood of the fixed point. We also discuss the existence of stable and unstable manifolds.
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 Hartman-Grobman and hyperbolic fixed points
10:36 Stable and unstable manifolds
13:50 Example of stable manifold
![[2/8] Control for Societal-Scale Challenges: Road Map 2030 [Societal Drivers]](https://i.ytimg.com/vi/vrIqsWIJR20/mqdefault.jpg "[2/8] Control for Societal-Scale Challenges: Road Map 2030 [Societal Drivers]
This video explores the key societal drivers and challenges that face the world where control theory has a central role in future solutions. Examples include climate change, health and well being, smart infrastructure, and the sharing economy. This follows Chapter 2 of the Control for Societal-Scale Challenges: Road Map 2030 document.
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")
![Residual Networks (ResNet) [Physics Informed Machine Learning]](https://i.ytimg.com/vi/w1UsKanMatM/mqdefault.jpg "Residual Networks (ResNet) [Physics Informed Machine Learning]
This video discusses Residual Networks, one of the most popular machine learning architectures that has enabled considerably deeper neural networks through jump/skip connections. This architecture mimics many of the aspects of a numerical integrator.
This video was produced at the University of Washington, and we acknowledge funding support from the Boeing Company
%%% CHAPTERS %%%
00:00 Intro
01:09 Concept: Modeling the Residual
03:26 Building Blocks
05:59 Motivation: Deep Network Signal Loss
07:43 Extending to Classification
09:00 Extending to DiffEqs
10:16 Impact of CVPR and Resnet
12:17 Resnets and Euler Integrators
13:34 Neural ODEs and Improved Integrators
16:07 Outro")
![[8/8] Control for Societal-Scale Challenges: Road Map 2030 [Recommendations]](https://i.ytimg.com/vi/w5UrYC_OPIk/mqdefault.jpg "[8/8] Control for Societal-Scale Challenges: Road Map 2030 [Recommendations]
This video concludes the roadmap with recommendations and key take aways. This follows Chapter 8 of the Control for Societal-Scale Challenges: Road Map 2030 document.
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")
