Now, normally, your cost function has two parts, right?
But if you think about this, the logic itself, then essentially what minimizing cost function is,
it's like finding a compromise mathematically, right?
It's like a you know, in life, you try to find compromise when you want to have something and you
want to have something else.
But you can't have both because let's say you want to study like you want to have good grades, but
you also want to party a lot.
Right.
But you know that if you only party and you don't study, then you're not going to have good grades.
But maybe you also want to party and you don't care about the grades that much, but you care a little
bit.
So what you do, you you try to find some kind of compromise, right.
To try to find some kind of common ground.
So you party a little bit, but you study a little bit to get the grades that you're happy with.
So that's like a compromise, right?
You find a compromise.
And essentially by minimizing the cost function, which you're doing, you're finding that compromise
only in this case, it's quantifiable.
You are mathematically finding your compromise and it's precision compromise.
Right.
So you're finding your compromise precisely in terms of real numbers.
You're quantifying it.
It's not something abstract anymore, like in life or I'm just going to party a little bit and study
a little bit.
But it's like a precise way to find a compromise between something.
And essentially, if you had something else that matters when it comes to rockets and you want to minimize
that, then you could just add another part to this cost function.
I mean, let's say that you have a lander, right?
And you have this rocket engine and what you care about is noise.
You don't want your rocket to be too noisy.
If you apply a lot of thrust, then the noise of your rocket engine would go up.
But if you want less noise, then you have to apply less thrust.
And so you could also have something like this, like w 11 times a noise at the K plus one second.
The thrust that you apply at K will influence the noise that K plus one because nothing is instantaneous.
Right.
You hear you at sample K, you, you press the button so to speak, or the system gives a go ahead and
then with a small delay you will have the result.
Right.
So now you have three parts in your cost function.
It's not common, but you could do that.
Right?
So if you do that, then you have a cost function with 15 different variables.
And when you minimize the cost function, then what will you get you again?
You will get some kind of compromise.
You will find your jamen.
Then for the jamen, you will find this unique vector of 15 variables.
Right.
Five error variables, five thrust variables and five noise variables.
The unique combination that will make the J as small as possible.
And then error depends on thrust and also noise depends on thrust.
And then from there you will find again this unique sequence of thrust values.
Teekay Teekay plus one up until T K plus four transposed.
Then we make this row vector Entercom vector.
But essentially that's what you will get if you have three parts in your cost function.
In the end, by minimizing your cost function, you will get a unique set of thrust values that if you
were to apply them to your rocket, it would result in a compromise of minimizing errors, minimizing
thrust values and minimizing your noise.
And if you have something else, you have a fourth variable that you care about so much.
You can have four parts in your cost function.
I mean, it's up to you.
There is no limit.