Thank you for good videos on Koopman Operators can you suggest me some research paper to study more about truncation of koopman observables.Where I can find more material on this one.
Steve, Great series. I have a question. All this Koopman technology is about taking a nonlinear system and transforming it into a linear equation of higher order. But this is exactly what you can do to a Riccati equation, and Riccati equations occur everywhere throughout control theory. Are the results of a Riccati transformation a special case of a Koopman invariant subspace? PS Met and talked with Nathan Kutz a few months ago in Santa Fe. Send my regards. -- John Finn
That is a great question! I just recently heard about this possible connection from a collaborator, so we started looking into it a little more. Short answer is I'm not sure, but definitely a good lead to find a connection. That is great that you met Nathan -- I'll say hi!
@@Eigensteve Steve, I came to Koopman methods from the more standard adjoint methods for various applications. I have agreed to give a seminar (or two!) on Koopman methods at WSU in October, and I may need to talk with you or Nathan about some issues. Would you be available? Also, it must be the case that Riccati equations (including matrix Riccati) must be a \emph{very} special case of NL equations that can be transformed to a finite dimensional linear system. (E.g. cannot have limit cycles, chaotic attractor, etc.) I'm not sure of the relation between Riccati equations and your example with \dot{x_2}=\mu(x_2-x_1^2). - John
Is the optimal control, a local optimum or a global optimum? In a linear system, LQR controller gives the global optimum, but is that the same for a koopan linearized system?
![Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]](http://i.ytimg.com/vi/831Ell3QNck/mqdefault.jpg)
Tons of thanks for the very great lectures!
It is very impressive and helpful!
Awesome, glad you like them!
Dear Steve! Great playlist on Koopman analysis. A little difficult to find the right order to watch videos. Thanks!
Thank you for good videos on Koopman Operators can you suggest me some research paper to study more about truncation of koopman observables.Where I can find more material on this one.
Steve, Great series. I have a question. All this Koopman technology is about taking a nonlinear system and transforming it into a linear equation of higher order. But this is exactly what you can do to a Riccati equation, and Riccati equations occur everywhere throughout control theory. Are the results of a Riccati transformation a special case of a Koopman invariant subspace?
PS Met and talked with Nathan Kutz a few months ago in Santa Fe. Send my regards. -- John Finn
That is a great question! I just recently heard about this possible connection from a collaborator, so we started looking into it a little more. Short answer is I'm not sure, but definitely a good lead to find a connection.
That is great that you met Nathan -- I'll say hi!
@@Eigensteve Steve, I came to Koopman methods from the more standard adjoint methods for various applications. I have agreed to give a seminar (or two!) on Koopman methods at WSU in October, and I may need to talk with you or Nathan about some issues. Would you be available?
Also, it must be the case that Riccati equations (including matrix Riccati) must be a \emph{very} special case of NL equations that can be transformed to a finite dimensional linear system. (E.g. cannot have limit cycles, chaotic attractor, etc.) I'm not sure of the relation between Riccati equations and your example with \dot{x_2}=\mu(x_2-x_1^2).
- John
@@johnfinn9495 Sounds very interesting, and would be available to chat sometime. Next month is crazy, but maybe after that.
thanks for this education. one tip though: the red graphs are very hard to see on the black background.
Is the optimal control, a local optimum or a global optimum? In a linear system, LQR controller gives the global optimum, but is that the same for a koopan linearized system?
Can we apply koopman operator theory to systems with inputs ?
You have math I've never heard of before, love you in a totally non gay way. KNOWLEDGE!
cool, you can write reversely??!
reversed writing skill. Crazy!
I don't know if he does that, actually. He could be left handed and writing normally on a transparent board, then he just flips the video.
Wat