systemidentifying

System identification, or systemidentifying, is the process of building mathematical models of dynamic systems from measured input and output data. The goal is to produce a model that can predict the system's behavior under new inputs. Models are typically classified as parametric (with a fixed structure and a set of parameters) or nonparametric, and as white-box (physical laws known) or black-box (data-driven).

Common approaches include time-domain methods, such as ARX, ARMAX, and Box-Jenkins models, and state-space identification. Frequency-domain methods derive models from spectral data. State-space methods include subspace identification techniques (e.g., MOESP, N4SID) that estimate system matrices without explicit parameterization. Parametric methods often use prediction error or maximum likelihood criteria to estimate parameters.

Key steps include experiment design with persistently exciting inputs, model order selection, parameter estimation, and model validation. Identifiability concerns determine whether the data suffice to uniquely determine the model. Validation examines how well the model predicts new data, using residual analysis, cross-validation, and information criteria (AIC, BIC).

Applications span control engineering (process control, flight and automotive systems), robotics, economics and biology, where accurate dynamic models enable simulation, control law design, fault detection, and system optimization.

History and context: System identification matured in the 1970s and 1980s, with foundational developments by researchers such as Ljung. It intersects with statistics, signal processing, and control theory.