Controllability [Control Bootcamp]

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This lecture explores when a linear system is controllable. We begin with the simple test in terms of the rank of the controllability matrix on a few intuitive examples.
Chapters available at: databookuw.com/databook.pdf
These lectures follow Chapter 8 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com/Data-Driven-Sc...
Book Website: databookuw.com
Brunton Website: eigensteve.com
This video was produced at the University of Washington

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22 янв 2017

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Комментарии : 88

@her00000 3 года назад

"You get to control u." - Steve Brunton full-time control professor and part-time life coach

@suntzu1409 3 месяца назад

-- Sun Tzu, The Art of Recursion

@shahinmehranfar8213 4 года назад

Whatever field you are studying, Steve Brunton can make you understand and love Control . Best Regards professor.

@Sinanmmd 3 года назад

My field is Mathematical Biology and I fully understand what he explains. I have done research papers on control and stability analysis. The control I have applied is thoroughly similar to this and I'm very excited to learn more from professor Steve. Thank you so much for this Bootcamp!

@pradiptahafid 2 года назад

I watched his video as a supplement of SVD because I have been binge-watching Gilbert Strang. Right now I am on chapter 8 of his book and I really enjoy it.

@liboyan7010 Год назад

As far as I know, Prof. Brunton is the best professor for teaching.

@originalandfunnyname8076 Год назад

This is probably the best playlist on youtube. I wish everyone would teach like that

@feloria1862 3 года назад

I love this series you don't go too deep into the math to lose me lol. My professor has slides which are filled with equations and its just hard to keep up.

@Eigensteve 3 года назад

Happy to help!

@ginebro1930 4 года назад

Thanks for your time and effort put into this, many of us know the theory but in most cases there is lack of general view that gives us a really good intuition, wich in time is very necessary in practice.

@mktsp2 2 года назад

Seriously, best Control lecture, ever. Congratulations, professor, we want more!

@liboyan7010 Год назад

As far as I know, Prof. Brunton is the best professor for teaching.

@atithi8 4 года назад

This is a honest to goodness, great lecture series!

@liboyan7010 Год назад

As far as I know, Prof. Brunton is the best professor for teaching.

@realredspry 2 года назад

This playlist is amazing. I am a current incoming graduate student in ME Controls and these primers have been a lifesaver all semester. Thank you so much. I will be checking out all your Machine Learning content as well!

@sugumarprabhakaran 2 года назад

Thank you so much professor. You really do a great job of taking a difficult subject and making it intuitive and understandable!

@Drone.Robotics 4 года назад

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.

@akhilsimha5349 3 года назад

You are God !!! Your explanation sums up my whole semester in half an hour.

@raincloud763 2 года назад

I'm studying this because i'm about to enroll in graduate school in controls and actuators. Thank you Professor Steve.

@husseingharakhani8002 4 года назад

Amazing! Thank you, sir!

@muhammadalgifari2349 Год назад

very kind teacher:') thanks steve! I am a first year biology student. I starting realize that this is really hard subject yet interesting and motivating because your teaching style 🤩

@siksniper1996 2 года назад

This really helps ties things together for me!

@amitupadhyay3603 2 года назад

You are remarkable sir,you have changed my perspective about B matrix.

@seyedmohammadhosseinirachi72 2 года назад

Awesome! Danke Professor für tolle Erklärung

@mktsp2 2 года назад

I have some dirty windows at home. I found the right person at last!

@bo-shianchen5712 3 года назад

Remarkable explanation! Thanks

@yuweifu2765 3 года назад

Thanks professor. This is a great course.

@pentagon0073 3 года назад

Wonderful lecture sir, we want more lecture on inverted pendulum control from you

@linxu4397 2 года назад

Really helpful and inspired, thanks!

@Excalibur32 3 года назад

I am thoroughly enjoying this lecture series!

@Eigensteve 3 года назад

Excellent!

@liboyan7010 Год назад

As far as I know, Prof. Brunton is the best professor for teaching.

@amitupadhyay3603 2 года назад

Thanks allot , phenomenon presentation,pls continue such lectures.

@parfaitatchade961 3 года назад

Hi Steve, First of all, congratulations on your contributions. They are really very good. I would say that you have a gift for communication in addition to knowledge of mathematics. One question, is it possible to see the control system that you explain as a solving technique of optimization systems given an initial condition? Thank you very much, Parfait

@saulpasillero6142 3 года назад

You are really advanced my friend. Keep going and thank you for sharing knowledge. I hope I could reach like 0.1% of your knowledge.

@Eigensteve 3 года назад

That is really kind of you -- it is fun that we are all still learning together!

@yimingao5420 3 года назад

You are just amazing!

@MSECECE-is3gg 3 года назад

Steve you are remarkable ..... Thanx Mate Love from India

@user-dz6vl5eq8v 4 года назад

Thank you, Professor!

@Eigensteve 4 года назад

You are welcome!

@tiberthyn 4 года назад

Thank you!

@HD141937 3 года назад

The way that you can control multiple states with a single actuator reminds me of solving a Rubik's cube. At first sight it looks like controlling one state/ moving one tile to the right position will mess up another state or tile. Somehow there is a way to get everything right at the same time.

@nehadali3001 4 года назад

thank you

@brahimallal891 3 года назад

Just Amazing! Thanks a lot.

@Eigensteve 3 года назад

You are welcome!

@mauriciocarazzodec.209 Год назад

i'm in love with this dude's brain

@neobermeo 3 года назад

Thank you for these impressing lectures on control systems. Could you activate the automatically generated english subtitles for this lecture ? Thanks again, professor Brunton.

@dvinayakaathreya2204 Год назад

Hi Professor, I absolutely loved the bootcamp. Could you please let me know where I can learn control theory (online) in much more detail.

@mohamedashrf5259 4 года назад

Hello prof.Steve, i have a question. what if we transform the state space to the form of the eigen values and eigen vectors, and since the dynamics are decoupled in the A matrix we can check the B matrix if it has a zero element in it's row. and Thank you very much professor for this lectures, it helped my a lot understanding a lot of theories.

@Find555 3 месяца назад

Sir great video.Can you please recommend some controller hardware .

@yafesenessahiner4782 Год назад

Thank you so much

@snehamoypatra9786 4 года назад

Amazing

@ashkabrawn 4 года назад

So for underactuated systems ..coupled states in A improves controllability.

@Katavicta Год назад

@26:00 when you discuss cutting edge systems that decide non linear-controlability, does that include fuzzy systems?

@anhtieng5315 Год назад

Can you make a video about Ziegler-Nichols method for controller tuning please? Also... why cant we use routh hurwitz criterion to determine if the system is stable or not? I guess for that we need a system CLTF, right? Thank you very much and the set really helps me review

@DieselBoulder 2 года назад

My linear math terminology might be a little rusty, but shouldn't you technically take the transpose of curly C to be determining the column rank of it? Effecitvely it's the same as "row rank" but I don't think that's a real term.

@youssefdirani 4 года назад

So electronics speaking, just a resistor in the feedback loop would stabilize a linear system, right ?

@juanramontorresano2932 4 года назад

Your class is awesome. Just please use filled pens :)

@sohaibheraoui1965 2 года назад

Please you can explian the controllability with therome Kalman

@eduardodossantos3099 4 года назад

I have a doubt. Could I get some prior information of the controllability only by A and B matrix individual ? For example the rank of state matrix (A) means something about the controlability of this state ? To be more clear, if my system is 10x10 and the rank of the matrix A is 9 that means something ? Thanks !!

@Eigensteve 4 года назад

Absolutely, there is definitely info in the A matrix that can be useful. Check out this video on the PBH test for controllability: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-0XJHgLrcPeA.html. In this video, we show how the dimension of the degenerate eigenspace corresponding to each eigenvalue of A determines how many columns the B matrix must have. So you can't get the complete picture about controllability, but you can definitely get some useful information just from A.

@eduardodossantos3099 4 года назад

Thanks ! I will see your vídeo. Thanks for the attention !

@arunbali7480 2 года назад

Thank you for this impressive lecture sir I have a question, consider a Nonlinear Systems x_1dot = x2.g_1+f_1 x_2dot = u.g_2+f_2 y = x_1 where x_1 and x_2 are state variables f and g are unknown functions May be this system is not controllable if x_2.g_1 is counteracted by f_1 Sir please clear this point.

@ryanthorngren7458 3 года назад

Are you left handed and mirroring the video afterwards, or did you learn to write backwards like Leonardo DaVinci?

@anonymousowl5240 3 месяца назад

8:25 gave me 737 Max vibes. Love the series

@steafish780 11 месяцев назад

I'm a complete noob to this and maybe I got something wrong here but if you calculate the two resulting vectors for Ax and Bu and then add these vectors, how then would u influence x1 like you explain at 15:26? If say x is [3,4] and A is like in your example then Ax gives [7,8]. Let u be 0.3 and B [0,1] then Bu is [0,0.3]. Adding Ax to Bu then gives [7,8.3]. As you can see u only affects x2 but not x1. in this case a change in B is necessary for u to influence the resulting x1 as well.

@PCSExponent 2 года назад

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

@BangkokBubonaglia 2 года назад

I second this question. I really wish he would spend at least a few seconds discussing the case where the A matrix has repeated eigenvalues and you need a B matrix of more than 1 column to be controllable. What does that mean for curly C? It is very unclear.

@Policies2040 2 года назад

He knew the mind of engineers and try to form a group of interested topics

@Policies2040 2 года назад

Thank you sir

@kalyan5968 3 года назад

Hello Sir , I am working on a robotics project. I am making a 2 wheeled screw propelled robot. I got the state space equations through lagrange's. I checked for controllability its rank is coming as 5 . i took x,y,theta ,and their derivatives as states. That means the system is not controllable ? How do I proceed sir .please help with this .. i am facing difficulty .. i follow all of your lectures.

@hariprasadhparthasarathy6360 9 месяцев назад

So there maybe a better choice of B that would make the system controllable. Did you investigate that?

@isbestlizard 4 года назад

I wonder if boeing did any of this when figuring out how to make their MCAS system not crash the plane repeatedly

@Eigensteve 4 года назад

My understanding is that all vehicle control groups have excellent control theorists. I don't know about any one specific company, but controllability is a major topic in flight dynamics design and certification.

@laytonbaker 3 года назад

@@m.3041 control theory is extremely useful in so many engineering fields. There are more "model-able" systems than "unmodel-able" system in my experience. I would have to see the conference presentation in question but as a controls practitioner I have never encountered a system where we just threw are hands and said, "yep... this is too hard... better to just treat the system as a "mystery box" and use some PID control variant." Now sometimes simple using PID is good enough and the least expensive option... but the performance is generally not as good as model-based adaptive/predictive control approach. I have run into many complex systems that where using numerous disparate PID controllers didn't work well at all... and an MPC approach worked great.

@marwahot9207 3 года назад

you are look smart 🥺❤️

@shawnmcneill4920 3 года назад

7:40

@romanvancouver1464 3 года назад

23:44 what I heard was "Now what I get to do is I multiply this newbie..."

@nomnamecpp 3 года назад

I am fan

@Eigensteve 3 года назад

Awesome!

@grymreaper5829 3 года назад

well you just saved my ass for an asignment xD

@ahsanali-qc6vj 3 года назад

Sir. ẋ = Ax + Bu x(0) = xo u(t) = exp(-at), t >= 0 Assume (aI-A)^-1 exists. Please show why x(t) = (aI - A)^-1 B exp(-at)+ exp(-at)(xo-(aI - A)^-1 B). Can you please explain this to me