Controllability [Control Bootcamp]

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/...
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...
Book Website: databookuw.com
Brunton Website: eigensteve.com
This video was produced at the University of Washington

[@her00000]

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

[@suntzu1409]

-- Sun Tzu, The Art of Recursion

[@shahinmehranfar8213]

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

[@Sinanmmd]

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!

[@phafid]

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]

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

[@originalandfunnyname8076]

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

[@mktsp2]

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

[@liboyan7010]

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

[@feloria1862]

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]

Happy to help!

[@ginebro1930]

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.

[@realredspry]

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!

[@atithi8]

This is a honest to goodness, great lecture series!

[@liboyan7010]

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

[@akhilsimha5349]

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

[@raincloud763]

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

[@mauriciocarazzodec.209]

i'm in love with this dude's brain

[@Excalibur32]

I am thoroughly enjoying this lecture series!

[@Eigensteve]

Excellent!

[@liboyan7010]

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

[@muhammadalgifari2349]

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 🤩

[@saulpasillero6142]

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]

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

[@mktsp2]

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

[@amitupadhyay3603]

Thanks allot , phenomenon presentation,pls continue such lectures.

[@amitupadhyay3603]

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

[@sugumarprabhakaran]

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

[@HD141937]

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.

[@pentagon0073]

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

[@MSECECE-is3gg]

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

[@siksniper1996]

This really helps ties things together for me!

[@anhtieng5315]

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

[@Katavicta]

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

[@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.

[@АндрейЧегуров-ц8з]

Thank you, Professor!

[@Eigensteve]

You are welcome!

[@seyedmohammadhosseinirachi72]

Awesome! Danke Professor für tolle Erklärung

[@husseingharakhani8002]

Amazing! Thank you, sir!

[@brahimallal891]

Just Amazing! Thanks a lot.

[@Eigensteve]

You are welcome!

[@yimingao5420]

You are just amazing!

[@Find555]

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

[@parfaitatchade961]

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

[@yuweifu2765]

Thanks professor. This is a great course.

[@anonymousowl5240]

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

[@DieselBoulder]

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.

[@giovannaalvescarvalhogrigo8221]

Thank you much for your lecture

[@dvinayakaathreya2204]

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

[@sohaibheraoui1965]

Please you can explian the controllability with therome Kalman

[@linxu4397]

Really helpful and inspired, thanks!

[@steafish780]

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.

[@bo-shianchen5712]

Remarkable explanation! Thanks

[@eduardodossantos3099]

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]

Absolutely, there is definitely info in the A matrix that can be useful. Check out this video on the PBH test for controllability: kzbin.info/www/bejne/ZomteZqCp8iDm6M. 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]

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

[@Policies2040]

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

[@Policies2040]

Thank you sir

[@neobermeo]

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

[@ashkabrawn]

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

[@romanvancouver1464]

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

[@PCSExponent]

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

[@BangkokBubonaglia]

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.

[@nehadali3001]

thank you

[@arunbali7480]

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.

[@youssefdirani]

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

[@mohamedashrf5259]

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.

[@ct7391-w5k]

For a nerd: this is filth... so good

[@ryanthorngren7458]

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

[@tiberthyn]

Thank you!

[@yafesenessahiner4782]

Thank you so much

[@ML2011ML]

In simply word, B must be the combinations of all eigen vectors of A, that is, B can not belong to any sub eigen vector combinations of A for fully control of all eigen values of A.

[@kalyan5968]

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]

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

[@isbestlizard]

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

[@Eigensteve]

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]

@@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.

[@juanramontorresano2932]

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

[@snehamoypatra9786]

Amazing

[@marwahot9207]

you are look smart 🥺❤️

[@shawnmcneill4920]

7:40

[@ahsanali-qc6vj]

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

[@emmanuelameyaw9735]

"I've got a gallon of gas". Economists here, that's your budget constraint.😀

[@grymreaper5829]

well you just saved my ass for an asignment xD

[@nomnamecpp]

I am fan

[@Eigensteve]

Awesome!

[@343906919]

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[@mozayn2378]

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[@mozayn2378]

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[@userjdufer466]

Thank you!