It looks like the intention of putting the build plans online and open sourcing it never materialized...too bad. Would have been nice to at least have an overview of the key design decisions and parts/materials used to help in making something similar. So far I haven't found any diy attempts to replicate the Ascento or Diablo, this one being the closest I've seen so far.
Nice lecture! May I ask you from which textbook did u took this treatment? Particularly I'm interested in the closed-loop form part of slide 32. Thanks for replying :-)
If you mean that c1 in the formula should be replaced with c2, then no. Note that lambda2 is obtained as (minus) the integral of lambda1. And lambda1 has previously been determined to be a constant c1. Integrating a constant amounts to multiplying it by the time (and allowing for a nonzero initial condition brings in the constant c2). Does it help?
At minutes 20.32(in block diagram. 1. Can you explain u(t) & v(t) , x-hat and w(t) 2. which two of them are input of Kaman filter 3. And which input making fool the kalman filter?
Great video! Question: For the generation of Q_barbar and T_barbar, the matrixes C_til'*Q*Ctil and Q*C_til must be calculated. However, when doing so, there is a dimensional mismatch and matrices cannot be multiplied.
Very useful video. Thank you. At the end you mention a next lecture that covers "numerical optimal control". I can't find it on your channel though. Does it still exist?
In general, if DP algorithm depends on discretization and interpolation in continuous state space and input space when solving a discrete time, finite time optimal control problem, does it yield a suboptimal solution?
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.
Thanks for the video. At 5:19 When you enumerate the cost function, I notice you use the total derivative to expand the summation term, which contain the derivative of x_k, u_k and λ_k. But WHY don't you use the same trick for initial time term, where you just retain the dX_i term. The same thing you did for terminal time term, where you just retian dX_N term. OK, I'm kind of figure it out. The reason why you skip the u_N is because u_N is not the parameter of terminal term. The reason why you skip the λ_1 term is because λ_1 is the co-state for x_1 = f(x_0, u_0) which is meanless. Am I corret?
Great lecture! I have a question about the Caveat. The value alpha''(0) = d1^2 + ... , where d = (d1, d2) and alpha''(0) means alpha'' evaluated at alpha = 0. Since alpha''(0) = 0 for some d1, namely d1 = 0, the sufficient condition is not satisfied. Hence alpha = 0 need not be a minima. So, why was this assertion, that alpha = 0 minima when checked using the directional derivative, made?
Thanks for the video! At 5:59 I'm not sure why we can "separate" the dJ'_i = 0 into all those 5 separate equations for all the "yellow" expressions. I tried reading the notes but still didn't get it. Could you please point me to some theory or explanation behind this which I could research? Thanks.
Vladyslav, sorry for a delay in response. But you'd better ask during an in-person lecture or seminar. After all, that is their purpose. I am not checking RU-vid frequently and regularly. As for your question: there is nothing very deep about the procedure, it is just that we enumerate all the variables upon which the cost function(al) depends and we want to find expressions for derivatives of the cost with respect to all these variables. WIth hindsight, we group these variables according to their origin (states, inputs, costates, and initial and final states separately) because then it turns out that the resulting formulas are "nice". You are not really expected to demonstrate this procedure. I do not think you will encounter the need to reproduce it in a different setting too often. But I wanted to show it here so as nothing is left in the dark in the derivation. This way you can check every possible typos I could have introduced.
