Editing System identification (section)

== Overview ==
A dynamic mathematical model in this context is a mathematical description of the dynamic behavior of a [[system]] or process in either the time or frequency domain. Examples include:

* [[physical system|physical]] processes such as the movement of a falling body under the influence of [[gravity]];
* [[economic system|economic]] processes such as international [[trade]] markets that react to external influences.

One of the many possible applications of system identification is in [[Control theory|control systems]]. For example, it is the basis for modern [[data-driven control system]]s, in which concepts of system identification are integrated into the controller design, and lay the foundations for formal controller optimality proofs.

===Input-output vs output-only===
System identification techniques can utilize both input and output data (e.g. [[eigensystem realization algorithm]]) or can include only the output data (e.g. [[frequency domain decomposition]]). Typically an input-output technique would be more accurate, but the input data is not always available. In addition, the final estimated responses from arbitrary inputs can be analyzed by investigating their correlation and spectral properties.<ref>{{cite book |last1=Ljung |first1=Lennart |title=Modeling and identification of dynamic systems |date=2021 |publisher=Studentlitteratur |location=Lund |isbn=9789144153452 |pages=221 |edition=Second}}</ref> 

===Optimal design of experiments===
{{Main|Optimal design#System identification and stochastic approximation}}
The quality of system identification depends on the quality of the inputs, which are under the control of the systems engineer. Therefore, systems engineers have long used the principles of the [[design of experiments]].<ref>Spall, J. C. (2010), "Factorial Design for Efficient Experimentation: Generating Informative Data for System Identification," ''IEEE Control Systems Magazine'', vol. 30(5), pp. 38–53. https://doi.org/10.1109/MCS.2010.937677</ref> In recent decades, engineers have increasingly used the theory of [[optimal design|optimal experimental design]] to specify inputs that yield [[efficient estimator|maximally precise]] [[estimator]]s.<ref>{{cite book|title=Dynamic System Identification: Experiment Design and Data Analysis|last1=Goodwin|first1=Graham C.|last2=Payne|first2=Robert L.|publisher=Academic Press|year=1977|isbn=978-0-12-289750-4|name-list-style=amp}}</ref><ref>{{cite book|title=Identification of Parametric Models from Experimental Data|last1=Walter|first1=Éric|last2=Pronzato|first2=Luc|publisher=Springer|year=1997|name-list-style=amp}}
</ref>