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.
Is there a course or material or underlying theory on controller parameter optimization instead of optimization over signals (for non PID controllers)?
No course matearial on that topic yet, sorry. You may want to have a look at our entry at Matlab Central www.mathworks.com/matlabcentral/fileexchange/42845-structured-mimo-h-infinity-design-for-a-dual-stage-platform-using-hifoo-and-hinfstruct. This is accompanying our paper dx.doi.org/10.1016/j.mechatronics.2013.08.003. The references in the paper can give you some directions too. Good luck.
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?
I am not sure if I understand the question but if you are asking for some justification of the form of the cost function, you may have a look at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-26sP4QIXgVA.html.
