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.
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.
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.
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..."
@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".
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 :-)
Fun fact. Pontryagin got permanently blind at age 14. He performed all of his groundbreaking research in optimal control while totally blind.
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.
Exactly, it schocked me as well.
Unbelievable....
Getting blind doesn't sound very fun.
sir grateful, you have explained it in 18 minutes, what others have not been able to in 3-4 lectures of hours
Cool, cool. I recognize some of those words.
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.
Is the preceding lecture on calculus of variations uploaded?
Great video!
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?
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.
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?
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..."
@@aa4cc Thanks for the reply and the reference (and the video). Downloaded a copy of Sussmann.
What is definition of state an costate in optimal control?
costate is just p, function of the same dimension of the state
@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".
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 :-)
@@aa4cc No problems! Thank you so much for the videos--a nice explanation of optimal control.
Please, I want to speaking with via Telegram or Email 📤
I need a references about this, please.
moodle.fel.cvut.cz/mod/page/view.php?id=141003
@@aa4cc thanks
I like ur accent
I am curious to hear how you would characterize it :-)