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‫Welcome back.

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‫So how did we transmit information about our cost function and our constraints to our saw?

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‫Well, both kewpie soldiers and quite brag, they assume that your cost function is in this form, including

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‫this one half year, and that your constraints they are in this form in the car course.

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‫I showed you a simple example our quadratic cost function in which Delta You Global was a two dimensional

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‫vector.

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‫This cost function was subject to constraints that looked like this, and then we could rewrite them

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‫in this form here.

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‫You can see that on the left side of the inequality sign, you have this matrix here and on the right

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‫side, you have this vector here.

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‫In principle, if your constraints are linear, then this matrix and this vector, they give you all

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‫the information you need about your constraints, except that you won't be able to tell if this sign

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‫here, whether it's like this or like this, you won't know that if you just look at this matrix and

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‫this vector, that's why kewpie solvers and quite POC insist that your constraints have to be in this

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‫form.

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‫Where this inequality sign points to the left, it's less than or equal to.

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‫But in our case, it points to the right.

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‫However, we can easily change that if we multiply both sides by minus one.

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‫If we do that, then this matrix and this vector, they will be like this.

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‫You will have minus signs here distributed among their elements.

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‫And then this sign here, it will change its direction.

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‫And now you have rewritten your constraints in the right form, and then we will call this Matrix G

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‫and this vector H.

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‫And that's exactly what Kewpie Solvers and quant project need.

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‫And so in order to give all the necessary information to the solver about the cost function, you would

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‫need to give it your h double bar matrix and your small F transposed.

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‫And in order to give the solver all the information it needs about your constraints, you simply give

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‫it your G Matrix and your H vector.

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‫Once you give the solver these four things, it will know exactly what kind of cost, function and constraints

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‫it is dealing with based on that information.

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‫It will return a solution that minimizes your cost function and respects your constraints.

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‫Note that in kewpie solvers, we also had to transpose our H vector because both the H vector and small

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‫have transposed they had to be role vectors small.

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‫If transposed, he's already a role vector.

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‫So no need to transpose that.

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‫But as you can see, H is a common vector, but q p solvers needs H to be a role vector.

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‫So that's why I'm transposing it here in quite prog in MATLAB.

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‫It doesn't matter.

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‫You can have small f and then this h vector as Coleman vectors, or you can have them as role vectors

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‫as well.

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‫So quite prog in MATLAB in this sense is a bit more flexible.

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‫And so here you can see the syntax for kewpie solvers.

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‫You can see that you're using this function here.

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‫Sort of underscore kewpie.

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‫And then here you can see the syntax for quite proc.

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‫As you can see these two elements.

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‫They can be either role vectors small if transposed and h transposed or vectors, small F and H.

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‫And so in order to find your optimal solution, your delta you global that respects your constraints.

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‫That's what you need to do.

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‫You need to take your h double bar matrix, your small F transposed your G matrix and your h transpose

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‫vector and you need to put them here in this order.

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‫And as mentioned before, later, it turned out that in windows, if you put here solver equals Civic's

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‫OPPT, then kewpie solvers works better there.

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‫So that would be your fifth parameter here.

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‫Also note that kewpie solvers gives you the solution as a role vector.

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‫Later on, however, I need it to be a common vector.

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‫That's why I transpose it here.

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‫Quite broke in MATLAB gives me the solution built a global C as a code vector, so that's another small

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‫difference between them.

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‫But to both of them, you need to give the same h double bar matrix small if transpose g and then each

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‫transposed.

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‫And so that was the entire game here in the car course, we constrained a lot of things.

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‫We can shrink Delta, Delta, Delta, A Delta A and then also small x dot and small.

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‫Why don't we kept them between minimum and maximum boundaries?

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‫I covered extensively how to do it there, but it all boils down to one thing the game was always to

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‫put all your constraints in this form.

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‫G times delta you global less than or equal to, and then your h vector.

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‫That was the game.

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‫It was all about mathematical manipulation in order to, in the end, obtain your G Matrix, which you

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‫can see here and your H vector, which you can see here.

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‫So all we did was that we played around with our equations and we manipulated them mathematically in

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‫such a way so that by the end of the day, your constraints would be formulated in such a way that you

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‫will end up having your G Matrix and each vector.

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‫And then you simply gave them to your kewpie solvers together with a double bar and small if transposed.

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‫And then the solver will give you Delta you global c, which is this one here in green, which minimizes

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‫your cost function and respects all your constraints.

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‫And so in this course, you have a drone, you have four motors, and these four motors have a minimum

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‫and the maximum angular velocity during the flight.

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‫Each model needs to have an omega that stays between your omega minimum and omega maximum.

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‫You cannot go below omega minimum and above omega maximum.

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‫So these are the constraints that we have to respect in this course.

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‫However, from the mathematics point of view, the goal is exactly the same.

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‫You have to obtain this form G times delta your global less than or equal to and then your H vector,

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‫and then you simply take your G Matrix and each vector and you give it to kewpie solvers together with

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‫your h double bar matrix and small f transposed.

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‫And then the solver will give you a solution.

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‫Delta your global c that minimizes your cost function and respects your constraints.

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‫We will simply have to do some smart mathematical moves to achieve that, and we will start doing that

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‫in the next video.

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‫Thank you very much.