# How to find the input output relation of an unknown non-linear system?

Hi friends,
I have a system (with unknown properties) which takes an input vector of length 10 and outputs a vector with length 6.

I select Inputs vector 'I' which is a 1000x10 matrix, : 1000 samples of 10 elements. And outputs vector 'O' is a 1000x6 matrix,: 1000 samples of 6 elements.

I just want to find input output relation ie system identification.
How can I do this using neural network toolbox in matlab?

-Devanand T

You can try. Depending on what your end goal is a NN may or may not help. In general what you would do is setup a NN with 10 inputs and 6 outputs. The number of intermediate layers and nodes in those layers you would have to play with to find what gives you good results. You would then divide your 1,000 samples into a training and verification set (probably something like 800/200 split) and proceed training/testing it to see if you can find a relation.

The problems you might have:

1.) If in the end you want to be able to write down some mathematical expression for the relation you aren't going to get that from the NN. What you will end up with if it works is a NN that can predict the output from inputs but how it is doing that will be "magic".

2.) If the samples are memory dependent training it will be much more difficult. Does the output vector depend only on the current input vector or do the last X input vectors also have some influence on the output? If the system does have memory you can account for this by also giving the NN the last X input vectors or some of the previous output vectors but the whole thing starts to get more convoluted.

The problems you might have:

1.) If in the end you want to be able to write down some mathematical expression for the relation you aren't going to get that from the NN. What you will end up with if it works is a NN that can predict the output from inputs but how it is doing that will be "magic".

2.) If the samples are memory dependent training it will be much more difficult. Does the output vector depend only on the current input vector or do the last X input vectors also have some influence on the output? If the system does have memory you can account for this by also giving the NN the last X input vectors or some of the previous output vectors but the whole thing starts to get more convoluted.
Thanks for the reply first of all..... Regarding problem 1) ie an output input relation equation, other than NN can you suggest some method...
And also present output depends only on present input...no memory property for the system.