__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. *

*Programme*

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*1. From data to model*

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

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*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.

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*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.

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*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.

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*5. Applications
and discussion of real world problems.*

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*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.