Course description


The model-based approach to control systems design calls for analytical description of the process to be controlled. Usually, the model is worked out by resorting to appropriate correlations or physical laws capturing the relationships among the variables of interest. However, it is a common experience that the obtained model suffers from uncertainty.

Identification methods enable to estimate unknown parameters and/or unknown signals, or the complete process model, by squeezing the information hidden in experimental data drawn from measurements of the process variables.

A main rationale to evaluate the quality of an estimated model is to assess its predictive capability. This is why prediction theory is an important preliminary step. Among the topics covered by the course, Kalman filter theory, a major engineering achievement, will be thoroughly studied as a tool for the identification of the state of a process from input-output measurements.


The course consists of about 60 hours of theoretical lectures and 40 hours of tutorial classes.




1.     From data to model

Physical laws in engineering and science. Models for filtering, prediction and control. Accuracy and complexity.


2.     Dynamical models of stationary processes,spectral analysis and prediction

Input-output models for time series and dynamical systems (AR,MA,ARMA,ARX,ARMAX). Correlation and spectral analysis. Canonical representation of stationary time series. Whitening filter and optimal predictor.


3.     Identification

Black-box identification via LS (Least Squares) and ML (Maximum likelihood) methods. Model complexity selection, with cross-validation, FPE (Final Prediction Error), AIC (Akaike Information Criterion) or MDL (Minimum Description Length) techniques.Yule-Walker equations and Durbin-Levinson algorithm. Spectral estimation. Time series analysis. Use of ARX and ARMAX models in control with minimum variance algorithm. Recursive identification methods (RLS,ELS,RML). Adaptation via forgetting factor techniques. Estimation of state-space models from data.


4.     Kalman filtering

The state estimation problem. Filtering, prediction and smoothing. The Kalman filter. Steady-state filter. Kalman prediction vs input-output prediction. Extended Kalman filter.



5. Applications and discussion of real world problems. 



Identification Laboratory

Data analysis and model identification are nowadays subjects of several software tools, used both for academic and industrial purposes. The laboratory classes aim to help students familiarizing with these tools, and in particular with the Matlab Identification Toolbox.