Sum Of Series variables from Vector.

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.

[Walter Roberson]

In z[2] your x0 is 0;2 but in z[3} your x0 is 0;0 ??

[Mustafa Sereflioglu]

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 ,,....

Answer 1

[Stephen23]

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);

[Mustafa Sereflioglu]

Thank you very much for you answer :)!

I noticed that I can present my problem in this way as well:

For exmaple z[1]:

i need to create this kind of Function a, automatically:

a = @(z) ,

the problem is, how can i generate the function a for z[2] automatically as well. For z[2] the generated function has to be:

a = @(z)

the reason why i need the function like this is because i need to use it for the fmincon function.

z = fmincon(a,z,A,b,Aeq,beq,lb,ub,nonlcon);

if there is a completely different way for this, just let me know. I would be very thankfull.

[Stephen23]

Your comment doesn't seem to have any relevance to my answer.

My answer already uses a simple loop to process up to n, exactly as your question requested.

[Mustafa Sereflioglu]

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]

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.