Armand,
To model a system using system identification, one approach commonly used is the so called prediction error approach, which consists in minimizing some cost function (usually quadratic) of the prediction errors defined as the difference between the response of the system and the response of the model.
For instance, when the model is linear in the parameters and the sum of the squares of the residuals (prediction errors) is chosen as the cost function, this leads to a least-squares approach, and this means that relatively simple and numerically robust algorithms can be used to estimate the parameters.
I am not completely sure, but it seems to me that the prediction error approach corresponds to a maximum likelihood one. Anyway, a good book on this subject is the one by Ljung called "System Identification: Theory for the user". I am sure you will find the answer there.
