Controllability, Reachability, and Eigenvalue Placement [Control Bootcamp]

This lecture explains the equivalence of controllability, reachability, and the ability to arbitrarily place eigenvalues of the closed loop system.

These lectures follow Chapter 8 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

This video was produced at the University of Washington

[alessandrodestro]

Thank you so much for this series, crystal clear how you go from theory to practical examples. Keep up this wonderful way of sharing knowledge and making it super understandable. I'm a student of automation at university and we don't lack the theory concepts but sometimes what we need is the big picture to really have comprehended. I shall follow all the super work you have done!

[kidcasco]

Thank you very much. This content and presentation is is first rate. You've brought me to a new level in my professional development. Cheers Dr Brunton.

[Drone.Robotics]

Thank you Sir....I have seen the whole playlist and it cleared a lot of my concepts about control theory. Your videos are just great and your way of teaching complex things in simple manner is appreciable. Thanks Again.

[zanubiadepasquale]

I wish I knew this playlist when I started studying control. Illuminating. Thank you

[leighstanger]

I'm about to embark on an active magnetic bearing control adventure and these lectures are invaluable. Thank you.

[ZhengQu]

What is this -1 "thumbs down"? The video is so good that youtube starts to do thumbs up in its own way...

[roblarssen]

I think there is a minor ambiguity in the definition of reachability. How you defined it at 5:33 seems to imply that giving u(t) instantaneously at time t will instantaneously drive the state to xi at the same time t. Whereas my understanding is that what reachability R_T means is there is a time-varying input function u(t) defined on [0, T] such that if you started at x(0) you will have x(T) = xi (note time = big T)

[JannCristobal]

damn. how do you draw such a perfect sphere

[sandippaul]

Is there any lecture series for more rigorous analysis on nonlinear control systems?

[王超-ov]

Hi, Steve, Thanks for your great explanation. Can I ask that does the system has to be controllable first, then it can be stablized with a state feedback control. If yes, is any mathmatical proof for this. Or is there any book decripting this issue?

[hessmanuel]

Hey Steve Brunton, although this video is very old I hope you're still reading it. I have a system with 4 states and i would like to show the influence of u on the states. I have now calculated eig(gram(sys, 'c')) and get the vector [0.0001
0.0064 0.0572 3.3803] . Do I see it correctly that I have a much smaller influence on x(1), than on x(2)? If this is not the correct way, what would you suggest instead?

[sabaaminolroaya]

hi . thanks a lot . I needed your videos for my thesis . please make videos for hamilton - jacobi - bellman equation and dynamic programming . thank you so much .

[alexboche]

Something seems weird in the def of reachable set. Is the t in u(t) supposed to be prior in time to the t in x(t) = ξ ?

[PCSExponent]

If B is an n×q matrix, how will the curly C matrix become n×n to check its rank?

[smallwang]

Can anyone be kind to tell me that why the pole is eigenvalue in 3:04😃