MODEL IDENTIFICATION AND DATA ANALYSIS

Master course in Automation Engineering

Credits 10

ProfessorS.Bittanti

Objectives

Themodel-based approach to control systems design calls for ananalytical 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 toestimate unknown parameters and/orunknown signals, orthecomplete 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 anestimated model is to assessits predictive capability.Thisis why prediction theory is an important preliminary step.

Among the topics deal twith,Kalman filter ingtheory,amajor engineering achievement, will be thoroughly studiedasa too lfor the identification of thestate of aprocess fromi nput-output measurements.

Program

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 dynamicalsy stems(AR,MA,ARMA,ARX,ARMAX).Correlation and spectralanalysis.Canonical representation of stationary time series.Whit eningfilter and optimal predictor.

3.     Identification

Black-boxi dentificationvia LS(Least Squares)and ML (Maximum likelihood)methods.Model complexity selection, with cross-validation, FPE (Final Prediction Error), AIC (Akaike Information Criterion) or MDL (MinimumDescriptionLength)techniques.Yule-Walkerequationsand Durbin-Levinsonalgorithm.Spectral estimation. Time series analysis.UseofARXeARMAXmodels in control with minimum variance algorithm. Recursive identification methods(RLS,ELS,RML).Adaptationvia forgetting factor techniques.Estimationof state-space models from data.

4.     Kalmanfiltering

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

5.Applications withth e discussion of real world problems.