1.1 Elements of System Identification

Mathematical models of systems (either natural or man-made) play an essential role in modern science and technology. Roughly speaking, a mathematical model can be imagined as a mathematical law that links the system inputs (causes) with the outputs (effects). The applications of mathematical models range from simulation and prediction to control and diagnosis in heterogeneous fields. System identification is a widely used approach to build a mathematical model. It estimates the model based on the observed data (usually with uncertainty and noise) from the unknown system.

Many researchers try to provide an explicit definition for system identification. In 1962, Zadeh gave a definition as ...

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