Systems Identification vs. Model identification

"However, still the problem of system identification has not been completely solved.
Consequently, nowadays new ideas and methods to solve the system identification
problem or parts of it are introduced." Keesman 2011.

We can say that the ultimate goal of science is building models, mathematical modeling is one of the means to achieve this goal, the promising is to apply more symbolic methodologies once this is the way we think. However, as always, life is not easy. Behind this challenge, new ones come out. One of the is system identification, sometimes referred to as model identification, apparently model identification is used more in Italy, further, it seems to be a broader concept, having system identification as a special case. 

The challenge that arises is based upon the fact that besides we might know how a system model looks like, in general we do not know the parameter values, for instance, what demands methods to find them from experiments. Maybe a nice way to see it is if you know the basics of music theory. Besides a symphony is complex, it is built upon simple chords, in general 8, but some musicians rely their works on just three chords; e.g. I, IV, and V. If you hear a song, you suppose to identify the chords, given you know them. However in real life it does not happen so easily. If you ask ten guitar players to transcribe a song you like, this is highly possible they will disagree, especially on subtle differences such as G and G7. In this case we can say they have failed to identify the system model, this is so an identifiability problem, they know the model in general, but details cannot be filtered out. 

In general, system identification consists of three basic steps: experiment design and data acquisition, model structure selection and parameter estimation, and model validation [1]. System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system [2]. 

Traditionally system identification is based on mathematics, however new trends are applying what can be kept by the name of computational intelligence such as neural networks.  

References cited

[1] Karel J. Keesman, System Identification: an introduction, Advanced books in control and signal processing, Spring, 2011.

[2] Lennart Ljung, System Identification: theory for user, Second edition, Practice hall information znd system science series, 1999.