Sum Of Series variables from Vector.

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Mustafa Sereflioglu
编辑： Stephen23 2020-6-8
Hello everyone,
I know this text seems to be long, but it is not. Just for clarification. Skip to [3] to see the Problem. Please help me :)!
[1] Description of the Problem:
Assume that there is a Vector called z=[ ]; this is a flexible Vector that means if i need for my
"x0" "u0"
system for example: z[1]. z is gonna be z=[ 1; 1; 3]; (1)
"x0" "u0" "x1" "u1"
if i need for my system z=[2]. z is gonna be z=[ 1; 1; 3; 0; 2; 0 ]; (2)
"x0" "u0" "x1" "u1" "x2" u2"
z[3] z=[ 1; 1; 3; 0; 0; 5 ; 7; 2; 0;]; (3)
and so on...
I need to make a function of
if z[3] = f(x0,u0,x1,u1,x2,u2) (3')
if z[2] = f(x0,u0,x1,u1) (2')
and so on...
to bring light into the dark our vector x0 would be z(1:2);
u0 would be z(3);
x1 would be z(4:5);
u1 would be z(6);
and so on...
Furthermore there are also 2 more matrices (Q and R, they are given), but they will not change over time. Q has the Dimensions of 2x2 and R 1x1.
[2] Goal:
The goal is to take the and the from the z vector and to build a automatic generated function in the following form.
for the example of z[2]:
f(x0,u0,x1,u1) = +
or z[3]:
f(x0,u0,x1,u1,x2,u2) = + +
[3] My idea:
i wanted to do it with the sum of series where the summation index will be i (to build the individual and ).
for z=[2] (see. [2]),;
f(x0,u0,x1,u2) = (4)
Now, i just have to fill the individual and to get the Solution. Just like:
x0 u0 x1 u1
f( z(1:2) , z(3), z(4:5), z(6)).
i really dont know how to build the function (4) in Matlab with n (depends on system) variables.
Sincerely yours,
M.S.
  2 个评论
Walter Roberson
Walter Roberson 2020-6-7
In z[2] your x0 is 0;2 but in z[3} your x0 is 0;0 ??
Mustafa Sereflioglu
Mustafa Sereflioglu 2020-6-7
the elements of are not relevant. Knowing that for exmaple the vector is builded trought z(1:2) is important and so on... just like placeholder to show, which lines of the vectors are ,,....

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Stephen23
Stephen23 2020-6-7
编辑：Stephen23 2020-6-8
Why not just use a loop?:
Q = [1,2;3,4];
R = 5;
z = [1;1;3;0;0;5;7;2;0];
%
X = [z(1:3:end),z(2:3:end)].';
U = z(3:3:end).';
n = numel(U);
F = nan(1,n);
for k = 1:n
F(k) = X(:,k).'*Q*X(:,k) + U(:,k).'*R*U(:,k);
end
F = cumcum(F);
  4 个评论
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Mustafa Sereflioglu
Mustafa Sereflioglu 2020-6-7
Thank you Stephen Cobeldick for replying,
i really did not get it. I'm trying to learn matlab since two weeks and i am not familiar with all functions!
Can you explain a bit more detail, please?
using your function:
for k = 1:n
F(K) = X(:,k).'*Q*X(:,k) + U(:,k).'*R*U(:,k)
end
will give me the Solution of every k iteration that means the Solution from every state first for z[1] (only consists of und ) and then if the Input was z[2] your function will safe the solution of z[1] and calculate z[2] but only consider & .
That is not what i search for.
I need the whole automatically generated function in dependence of z.
in the form i wrote earlier.
And i dont know how i could use your function for fmincon. I dont see any similarites between what i search for and your function.
for example z[3] i search for a exact function like this:
Function = @(z)
(1)
and your answer is (2):
Q = [1,2;3,4];
R = 5;
z = [1;1;3;0;0;5;7;2;0];
%
X = [z(1:3:end),z(2:3:end)].';
U = z(3:3:end).';
n = numel(U);
F = nan(1,n);
for k = 1:n
F(K) = X(:,k).'*Q*X(:,k) + U(:,k).'*R*U(:,k)
end
In my case i have a function of (z) . In your case i have the solution of what i have written. I need the Function of itself and not the solution to work with it.
Sorry, if i have troubles to understand it, but between (1) and (2) are differences.
Thanks.
Stephen23
Stephen23 2020-6-8
编辑：Stephen23 2020-6-8
Your code is missing cumsum at the end. This is required because your formula for F(n) is just F(n-1) plus a new term. So we might as well just calculate all the terms once (there is no point in repeating them) and then get the cumulative sum of them. That is what my code does.
If you don't want to use cumsum then just add the terms in the loop, e.g.:
tmp = 0;
for k = 1:n
tmp = tmp + X(:,k).'*Q*X(:,k) + U(:,k).'*R*U(:,k);
F(k) = tmp;
end
If you want that code as a function, then just define it inside an Mfile:
https://www.mathworks.com/help/matlab/ref/function.html
For example:
function out = myfun(z)
... my code
out = sum(F); % you need this at the end!
end
and provide a handle of that function to fmincon, just as the documentation shows:
x = fmincon(@myfun,...)
Note that because fmincon requires the function output to be a scalar you will have to return a scalar from the function, e.g. the sum of F as I showed above.

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