The course is taught in English. The purpose of this course is to provide basic 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: Prova scritta (in aula); Prova pratica di laboratorio; Elaborato scritto individuale;

Exam: Written test; Practical lab skills test; Individual essay;

... The final assessment consists of an individual written test, about three hours long, to be performed in the computer laboratory using the MATLAB software tools, and it is aimed at evaluating the competencies of the student with reference to all the subjects of the course program. The examination aims at verifying the knowledge and the abilities listed as items from 1) to 5) in the "Expected Learning Outcomes" section: the proposed problems not only require to choose and apply the most suitable instruments, but also make indispensable the logical concatenation of the theoretical topics investigated during the course to correctly interpret and understand the numerical results provided by the software tools. The examination is typically made of a model building practice of an unknown system starting from given data and a second exercise on Kalman predictor and/or filter design and simulation for a given linear dynamic system. The candidate has to provide a clear report that includes the reasoning behind the computations, the main numerical results and their possible critical analysis. The maximum score of the exam is 32/30; about 60 per cent of this score depends on the evaluation of the model building practice. The test is closed books; the candidate is not allowed to use textbooks or notes, except the official formulary, directly provided by the teacher during the exam as .pdf file (and downloadable before the exam from the course web page). No other material is allowed, i.e., no personal notes, exercises, portions of MATLAB code or solutions of specific exercises, in complete or partial form, anyway coded.

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.

Modalità di esame: Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

The final assessment consists of an individual written test, about three hours long, to be performed using vLAIB and the "Exam" platform with the Respondus proctoring tool and the MATLAB software tools, and it is aimed at evaluating the competencies of the student with reference to all the subjects of the course program. The examination aims at verifying the knowledge and the abilities listed as items from 1) to 5) in the "Expected Learning Outcomes" section: the proposed problems not only require to choose and apply the most suitable instruments, but also make indispensable the logical concatenation of the theoretical topics investigated during the course to correctly interpret and understand the numerical results provided by the software tools. The examination is typically made of a model building practice of an unknown system starting from given data and a second exercise on Kalman predictor and/or filter design and simulation for a given linear dynamic system. The candidate has to provide a clear report that includes the reasoning behind the computations, the main numerical results and their possible critical analysis. The maximum score of the exam is 32/30; about 60 per cent of this score depends on the evaluation of the model building practice. The test is closed books; the candidate is not allowed to use textbooks or notes, except the official formulary, directly provided by the teacher during the exam as .pdf file (and downloadable before the exam from the course web page). No other material is allowed, i.e., no personal notes, exercises, portions of MATLAB code or solutions of specific exercises, in complete or partial form, anyway coded. The student has to show everything on the table, whose recording is requested in the Environment Video of the Lockdown Browser startup procedure.

Modalità di esame: Test informatizzato in laboratorio; Prova scritta tramite l'utilizzo di vLAIB e piattaforma di ateneo;

The structure and the contents of the exam are the same in the two modalities (online and onsite), which in any case must be considered as mutually exclusive according to the general rules of Politecnico. The online modality is detailed in the devoted section above. In case of onsite exam, everything detailed in the online modality holds, with the only difference that the exam will be held in the laboratory instead of using vLAIB and the Exam platform with Respondus.