1 00:00:00,650 --> 00:00:10,130 ‫Finally, once your embassy simplification has given you your seat to the Star Global, why max global 2 00:00:10,130 --> 00:00:11,350 ‫and why mean global? 3 00:00:12,020 --> 00:00:14,120 ‫Now we can use them in the main file. 4 00:00:14,690 --> 00:00:20,120 ‫So just like in section eight, here I compute my small f transposed. 5 00:00:20,690 --> 00:00:29,270 ‫And now if my constraints, which equals one meaning that I'm considering my constraints, then here 6 00:00:29,480 --> 00:00:32,480 ‫I create my CC matrix. 7 00:00:33,200 --> 00:00:40,430 ‫It's this one here you see, see till their star Global Times C double bar. 8 00:00:41,060 --> 00:00:45,950 ‫And then from that, I can create my g matrix that I need for my constraints. 9 00:00:46,580 --> 00:00:52,540 ‫And I simply take this CC matrix and I concatenate them like this. 10 00:00:53,150 --> 00:00:58,820 ‫And I have this minus sign here, because that's what you have in the G Matrix. 11 00:00:59,480 --> 00:01:05,780 ‫And so this g matrix here that we had derived some videos ago, it's this one here. 12 00:01:06,410 --> 00:01:15,110 ‫And now we also need to generate our H vector, which is this one here and this entire generation process. 13 00:01:15,470 --> 00:01:19,040 ‫It happens here with these two lines. 14 00:01:19,700 --> 00:01:23,120 ‫I multiply C Tilde Star Global Times. 15 00:01:23,450 --> 00:01:28,550 ‫A double circle flex times the augmented presence state vector. 16 00:01:28,700 --> 00:01:30,200 ‫So it's this term here. 17 00:01:30,860 --> 00:01:34,970 ‫Then this h one, it's y max global minus. 18 00:01:35,600 --> 00:01:38,420 ‫And then what you had received here. 19 00:01:39,050 --> 00:01:44,780 ‫So this is essentially your h one and then your H two that you have here. 20 00:01:45,440 --> 00:01:53,450 ‫It's minus y min global plus what you had here, what you had generated with these two lines. 21 00:01:54,110 --> 00:01:59,450 ‫So this one here, the second element, that's your H. 22 00:02:00,440 --> 00:02:05,660 ‫And remember this Y global star max and Y global star men. 23 00:02:05,930 --> 00:02:08,380 ‫And then your c till the Star Global. 24 00:02:08,960 --> 00:02:12,200 ‫They all came from your MPAC simplification function. 25 00:02:12,860 --> 00:02:14,360 ‫They are these ones here. 26 00:02:14,960 --> 00:02:21,050 ‫And once you have your H1 and H2, you can simply concatenate them like this. 27 00:02:21,680 --> 00:02:29,690 ‫And so you have your H vector and then once you have it, you also need to transpose it because your 28 00:02:29,690 --> 00:02:33,920 ‫kewpie solvers needs to have it as a role vector. 29 00:02:34,460 --> 00:02:41,140 ‫So this entry here, it's your role vector, the same thing like your small f transposed. 30 00:02:41,150 --> 00:02:42,770 ‫It's also your role vector. 31 00:02:43,340 --> 00:02:45,890 ‫And that's how you find your Delta U Global. 32 00:02:46,520 --> 00:02:47,510 ‫Is this one here? 33 00:02:47,510 --> 00:02:51,620 ‫Delta U global superscript c and then all this. 34 00:02:52,340 --> 00:02:57,380 ‫It's your solution that minimizes your cost function and respects all your constraints. 35 00:02:58,010 --> 00:03:05,810 ‫You put here your age double bar that you got from your MBC simplification function, then small if 36 00:03:05,810 --> 00:03:15,710 ‫transposed that you had calculated here and then your G matrix that you have from here and your h transposed 37 00:03:16,400 --> 00:03:17,390 ‫that you have here. 38 00:03:17,990 --> 00:03:24,920 ‫And then if you put here smaller equals CVS, except then it simply works better. 39 00:03:25,490 --> 00:03:31,040 ‫And then just like in section eight, you only extract the first delta. 40 00:03:31,040 --> 00:03:39,170 ‫You two, the first Delta you three and the first Delta you four and you discard everything else. 41 00:03:39,890 --> 00:03:48,620 ‫These are your previous two Q3 and Q4 values, and these are your new Q2, Q3 and Q4 values. 42 00:03:49,250 --> 00:03:53,030 ‫And then this block here, that's what you had in section eight. 43 00:03:53,210 --> 00:03:56,510 ‫That's when you choose not to consider MVC constraints. 44 00:03:57,200 --> 00:04:06,170 ‫Now you can see that here I have two brackets like this, and then here I only have one bracket. 45 00:04:06,800 --> 00:04:14,360 ‫The reason for that is that if I use the solver in order to compute my delta, you'll global, then 46 00:04:14,360 --> 00:04:15,410 ‫it's a roll vector. 47 00:04:16,010 --> 00:04:21,770 ‫And then I extract the first elements from this dual variable like this with one bracket. 48 00:04:22,370 --> 00:04:29,900 ‫But this role here, which we had in section eight, that's finding the solution using the gradient 49 00:04:29,900 --> 00:04:30,290 ‫method. 50 00:04:30,860 --> 00:04:34,760 ‫And this row here it gives me a column vector. 51 00:04:35,330 --> 00:04:41,330 ‫And so when you want to extract the first elements from your column vector, then you need to have two 52 00:04:41,330 --> 00:04:42,080 ‫brackets here. 53 00:04:42,650 --> 00:04:43,370 ‫And that's it. 54 00:04:43,640 --> 00:04:47,450 ‫Everything else in this code file is the same. 55 00:04:47,990 --> 00:04:55,210 ‫You calculate your Omegas, you go inside your plant, you get your new states and then you start with 56 00:04:55,220 --> 00:04:55,880 ‫a new loop. 57 00:04:56,240 --> 00:04:59,990 ‫And then starting from here, the animation code starts. 58 00:05:00,500 --> 00:05:05,360 ‫And there is also a course about how to create awesome animations in Python. 59 00:05:05,990 --> 00:05:09,150 ‫And now let's take a look at some of the results. 60 00:05:09,830 --> 00:05:13,490 ‫And let's see if our embassy constraints work. 61 00:05:14,060 --> 00:05:14,990 ‫Thank you very much.