How do you correlate 2 unique inputs to the 3 outputs given?

If I have a system with 2 influencing inputs (e.g. i1 & i2) and a combination of these two inputs will provide 3 outputs (e.g. o1, o2 & o3).

i.e. f(i1, i2) = [o1, o2, o3]

How can you extract the correct 2 input values that correspond with the 3 output values given?

Thanks

[Jose Marques]

Can you give more information or exemples?

[Ethan Gardner]

Yes, for example, if I provide this table of how the three output values vary with the input values, is it possible to extract the input values being given just the three outputs?

Is there an analytical approach to see how each o varies with i1 and i2 or is the best method some form of lookup table?

Many thanks.

Answer 1

[OCDER]

Use fminsearch to determine [i1, i2] that satisfies [o1, o2, o3] within a tolerance range.

Q&A: using fminsearch for functions with 2 input variables

Let's say a function (func) takes 2 inputs and returns 3 outputs.

function Out = func(In)
Out(1, 1) = In(1);
Out(2, 1) = In(1) + In(2);
Out(3, 1) = In(2);

Make an objective function (objfunc) that takes an input vector and returns a smaller scalar value the closer you are to the desired output (DesiredOut). Provide an initial guess for the inputs (InitGuess).

objFunc = @(I)max(abs(func(I) - DesiredOut));
Desired0ut = [1; 3; 2];
InitGuess = [1; 1];

Find the best inputs that minimizes objfunc.

BestI = fminsearch(objfunc, InitGuess)

BestI = 
  1
  2