The course is taught in English.
The purpose of this course is to provide basic theoretical methodologies and software tools for building mathematical models of linear and nonlinear (static or dynamic) systems from experimental data.
The student shall acquire the following knowledge and develop the following abilities:
1) Knowledge of main methods and software tools for building mathematical models (based on physical-laws or in form of difference equations, input-state-output equations or transfer functions) of linear and nonlinear (static or dynamic) systems
2) Knowledge of main methods and software tools for evaluating estimate reliability and model quality
3) Knowledge of basic theoretical properties of main methods for building mathematical models of static or dynamic systems
4) Skill in building mathematical models of linear and nonlinear systems exploiting both physical information and experimental data
5) Skill in evaluating estimate reliability and model quality
The following notions are essential: knowledge of the representations of linear dynamic systems (input-state-output equations, transfer functions) and of their fundamental properties (stability, controllability, observability); essentials of probability theory and statistics; basic concepts of linear algebra and Zeta transform. The knowledge of the MATLAB software environment is required.
Course topics and relative devoted time:
- Introduction to estimation and prediction problems. Main statistical estimation methods (least squares, weighted least-squares, maximum likelihood estimators, Bayesian estimators) and their basic properties (correctness, consistency, efficiency), with evaluation of parametric estimation error (18 hours)
- Set-membership estimation theory for different norm assumptions on noise, with evaluation of Estimate Uncertainty Sets and Intervals. Optimal and Central estimates, with evaluation of Feasible Parameter Sets and Parameter Uncertainty Intervals (7 hours)
- Introduction to Kalman filtering problem: dynamic one-step and multi-step predictors, dynamic optimal filter, steady-state one-step predictor and filter, nonlinear predictors and filters (11 hours)
- Identification of linear dynamic systems from input-output measurements: FIR, ARX, ARMAX and OE models. Predictive approach and models in predictor form. Asymptotic analysis of prediction-error identification methods. Least-squares method: probabilistic analysis, persistence of excitation, practical procedure. Recursive least-squares methods. Model structure selection and validation (whiteness test and residual analysis; FPE, AIC and MDL criteria) (18 hours)
- Identification of nonlinear dynamic systems from input-output measurements: statistical and set-membership methods. Neural networks: approximation properties, learning (6 hours)
Exercise sessions are focused on the development of both academic and applicative examples. Some other sessions (16 hours) are carried out in computer laboratories and are focused on modelling real-world static or dynamic systems (position transducer, hair dryer, water heater) and on Kalman predictor and filter design and simulation for a given linear dynamic system, using MATLAB toolboxes (Control System, System Identification, Neural Network based System Identification).
The following textbooks have been mainly addressed in the organization of the course:
- S. Bittanti, "Teoria della Predizione e del Filtraggio", VII edition, Pitagora Editrice Bologna, 2004 (in Italian)
- S. Bittanti, "Identificazione dei Modelli e Sistemi Adattativi", VI edition, Pitagora Editrice Bologna, 2004 (in Italian)
- T. Kailath, A. H. Sayed, B. Hassibi, "Linear Estimation", Prentice Hall, Upper Saddle River, N.J. (U.S.A.), 2000
- L. Ljung, "System Identification: Theory for the User", II edition, Prentice Hall PTR, Upper Saddle River, N.J. (U.S.A.), 1999
- L. Ljung, "System Identification Toolbox User’s Guide", The MathWorks Inc., Natick, MA (U.S.A.), 1988-1997
On the course web page www.ladispe.polito.it/corsi/MIC/ , teaching material is available about specific issues addressed in the course, like: lecture slides, laboratory exercises with proposed solutions, official formulary.
Modalità di esame:
Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.