‫Welcome back.
‫I hope you have thought about how to obtain this form for our constraints, as mentioned before, you
‫have this equation here.
‫You know that x global tilde, it equals all that.
‫But let's not only focus on this one here, your excellent tilde equals all that.
‫And so how would you extract the last three elements from this vector?
‫Well, we can use a similar matrix that we used in order to extract states that we wanted to have as
‫outputs.
‫For that, we used this see matrix.
‫But now we have an augmented state vector and we want to extract different things from there.
‫We want to extract you two zero, use three zero and you for zero.
‫And you can do it like this.
‫This is what you want to have.
‫You want to have this vector.
‫Then this vector here, that's your X1 till there.
‫And so you want to extract this element, this element, and also this element.
‫Therefore, you need a matrix here.
‫And this matrix looks like this.
‫This one here, it will extract you two zero for you.
‫This one here it will extract you three zero for you and this one here it will extract you four zero
‫for you.
‫And so let's called this matrix C tilde asterisk.
‫OK, but now you want to extract you two Q3 and Q4 from Excel, the two X2, the three and X2, the
‫four as well.
‫Well, how about if I do this trick?
‫This is my ex till the global.
‫It's this one here.
‫If I now create this matrix here, then this is what I will have.
‫I will have this thing here.
‫This c till the star.
‫That's this matrix here.
‫So if you think about the dimensions, then this vector has three rows and one column this vector here
‫it has nine rows and one column.
‫And so this matrix here it has three rows and nine columns.
‫And now I create a global C till the star like this, and it consists of these little C to the stars
‫here.
‫So for example, this one here, it's this one here.
‫Three rows and nine columns.
‫The same thing here.
‫This one, this one and this one, all of them are the same.
‫And of course, that also means that these zero matrices, they have three rows in nine columns.
‫And so if you position these small seats, all the stars along the diagonal here and then you multiply
‫this C to the Star Global by this x still that global vector.
‫Then the result is that each predicted augment the state vector.
‫It will be multiplied by this C tilde star matrix like this in this order.
‫That means that you will be able to extract you two you three u four from all of these vectors.
‫And so I'm going to name this one.
‫Why Star Global?
‫And so if I write it out, then this is how it looks like this one here.
‫It's this one here, and we can call it y one star.
‫Then this one here it will be this one here.
‫We can call it y two star.
‫Then this one here it will be this one here.
‫That's why three star and finally, this one here.
‫Well, it's going to be this one here.
‫And let's call it y four star.
‫And of course, this entire vector, it's this one here.
‫So with that, you can extract all the use from all the predicted augmented state vectors.
‫And so in a compact way, you can write it all like this y global star, which is this one here.
‫It equals C Tilde Star Global, which is this gigantic matrix times x till their global.
‫Which is this one here?