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

This course requires a heavy workload and is recommended only to highly motivated students with strong theoretical background and advanced programming abilities. In particular, 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", VIII edition, Pitagora Editrice Bologna, 2017 (in Italian) - S. Bittanti, "Identificazione dei Modelli e Sistemi Adattativi", VII edition, Pitagora Editrice Bologna, 2017 (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.

Lecture slides; Exercise with solutions ; Lab exercises with solutions; Video lectures (previous years);

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; a second exercise on Kalman predictor and/or filter design and simulation for a given linear dynamic system; a closed-book theory question on any topic of the course (proofs included), lasting about 20 minutes and worth 4 points, being the score of the entire exam set to 32 points. The candidate has to provide a clear report that includes the reasoning behind the computations, the main numerical results and their possible critical analysis. About 60 per cent of the score of the exam depends on the evaluation of the model building practice. The clarity of the notation and the overall accuracy in the report will also be taken into consideration to obtain the maximum score. There is the possibility of self-assessment and withdrawal without any penalty within 48 hours following the exam. If the student withdraws, the examination rating is recorded as “withdrawn”; otherwise, the examination rating is recorded and therefore the student is considered as “graded”. Only students who have never been graded in previous exam sessions (with any score, sufficient or insufficient) are exempt from the closed-book theory question; they will have the entire time available to carry out the other exercises, whose overall score in this case will be rescaled to 32 points. 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.

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.