Hi Joshua,
Looks like in this case both System identification as well as neural networks toolboxes could be of viable approaches.
As far as the neural networks you could capture the system response (time series) and then train a neural network (either a pattern network or a time series neural network if your intention is to predict ) and then deploy it for use.
In one of the cases I have experimented capturing data from a simulink model and trained a neural network pattern recognizer and then been able to infer what are the components causing a particular kind of response and have seen good results. How ever I want to keep you informed that you may have to generate a lot of data (unique learnable features for the neural networks) and training to get this working !
Hope this helps !
Sreeram Mohan
