Identification of dynamic systems

The problem addressed concerns the determination of an analytical model belonging to a given class, based on the knowledge of input/output signals. The dynamic behavior predicted by the model must be as close as possible to that of the process under consideration, in the sense of a criterion. There are two main classes of identification methods: non-parametric and parametric. In this course, we focus on parametric methods.

Any identification procedure proceeds as follows: Choice of experimental protocol, choice of model structure, choice of estimation method, validation of the estimated model. The aim of this course is to cover these different stages. More specifically, we begin with a presentation and critical analysis of the different structures used in parametric estimation. Then, among the various estimation methods available in the scientific literature, the ordinary least squares method, based on the minimization of a quadratic criterion, is discussed. The various validation tests are then presented. The course concludes with a chapter on the prediction error method.

Linear system dynamics, Sampled systems, Discrete control law synthesis, Digital signal processing.

The course content is as follows:
* Introduction and motivation: Presentation of objectives, review of non-parametric methods, definitions of auto and inter-correlation functions, power spectral densities and the theory of random variables.
* Model structure in identification: Presentation of ARX, ARMA, ARMAX, OE and Box-Jenkins structures, analysis of advantages and disadvantages. Analysis of advantages and disadvantages.
* The parametric estimation method of ordinary least squares. Presentation of the problem, quadratic criterion, minimization of the criterion.
* Quantifying the confidence of the estimate: Test of the whiteness of the prediction error, Input/output correlation tests, Confidence regions in parametric space, in the Bode and pole/zero planes.
* Prediction error method. Problem presentation and solution.
* Design office: Application of method tools to the case of a real process.

Automatic

[1]: "System identification: Theory for the user", L. Ljung, Prentice Hall, 1987.
[2]: "System identification" T. Söderström and P. Stoïca, Prentice Hall, 1989.