L7.1 Pontryagin's principle of maximum (minimum) and its application to optimal control

[@alphonsusadubredu]

Fun fact. Pontryagin got permanently blind at age 14. He performed all of his groundbreaking research in optimal control while totally blind.

[@aa4cc]

Unbelievable. I did not know it. Thanks. I tried to imagine this (doing some mathematics just in my mind with no pen and pencil, not to speak of a computer) a few times and... it is just incomprehensible... Such a hundred-percent mental concentration.

[@vitezslavstemberafemCalc]

Exactly, it schocked me as well.

[@Sungjuni]

Unbelievable....

[@manimusicka2]

Getting blind doesn't sound very fun.

[@yasirnaeem7192]

sir grateful, you have explained it in 18 minutes, what others have not been able to in 3-4 lectures of hours

[@friedrichwilhelmhufnagel3577]

Hello, at 01m35s you speak of the "previous lecture." Unfortunately I can not find a lecture indexed L7.0 or L6.9 or the like. Where may I find this previous lecture please? Thank you very much for this great video.

[@BooBaddyBig]

Cool, cool. I recognize some of those words.

[@scose]

Is the preceding lecture on calculus of variations uploaded?

[@wcottee]

Why at 8:23, x* is on both sides. If u is different (u vs. u*) wouldn't x be different as well ? What did I miss?

[@aa4cc]

Well, that is the key essence of Pontryagins principle that Hamiltonian is viewed as a function of three variables (x, u and lambda) as if these three were completely unrelated. We know that they are, but in the theorem we "pretend" they are not. A nice recapitulation of this "trick" is given in the paper SUSSMANN, Hector J.; WILLEMS, Jan C. 300 years of optimal control: from the brachystochrone to the maximum principle. IEEE Control Systems Magazine, 1997, 17.3: 32-44. doi.org/10.1109/37.588098 (I did my best to include this explanation in the video too, but maybe it was still not enough :-). They write "let us tell the story of how Hamilton almost got there himself, but missed, and Weierstrass got even closer, but missed as well..."

[@wcottee]

@@aa4cc Thanks for the reply and the reference (and the video). Downloaded a copy of Sussmann.

[@xiaoyandai9482]

hello, many thanks for your kind share. And could you please explain the final inequality about the optimal control law and the sat(u LQR) more?

[@aa4cc]

I was about to start explaining the stuff but I re-listened to what I actually recorded in the video and I am afraid I am not able to add anything to that explanation in the video. Let's perhaps do it the other way around: give me here your own interpretation of that statement and I could perhaps tell you if your understanding is correct.

[@kurtcobainsr]

Great video!

[@willyamsihotang6572]

What is definition of state an costate in optimal control?

[@halik919]

costate is just p, function of the same dimension of the state

[@lidacherif7545]

I need a references about this, please.

[@aa4cc]

moodle.fel.cvut.cz/mod/page/view.php?id=141003

[@lidacherif7545]

@@aa4cc thanks

[@drillsargentadog]

@13.10 "in vesser [?]--I mean English written..." What the heck is vesser? Was he trying to say "western" or "lesser" or something? Actually from later context it looks like he meant to say "western".

[@aa4cc]

Indeed, I wanted to pronounce "western". Sorry for the confusion. Honestly, now that I listened to it (again), I myself had troubles to decode the meaning :-)

[@drillsargentadog]

@@aa4cc No problems! Thank you so much for the videos--a nice explanation of optimal control.

[@engineer6054]

Please, I want to speaking with via Telegram or Email 📤

[@audiencianacional4385]

I like ur accent

[@aa4cc]

I am curious to hear how you would characterize it :-)