D1. Knowledge and understanding The student, at the end of the course, should know the advanced principles for the analysis of deterministic and stochastic discrete-time dynamic systems. Moreover, for the present module, the student should be able to select from the technical literature and engineering specifications, to design and to test the basic techniques for the parametric estimation and identification of stochastic dynamic models. D2. Applying knowledge and understanding The student should be able to carry out a complete and comprehensive analysis of the main properties of deterministic and stochastic discrete-time dynamic systems and should be able to design and implement parametric estimation and identification, and state estimation algorithms that use available data or data collected in real-time with reference to engineering application scenarios. D3. Making judgements The student should be able to evaluate, among several options, what's the best choice of parametric estimation and identification, and state estimation algorithms starting from requirements and considering technological constraints. D4. Communication skills The student should be able to describe in a clear and plain way the functionalities of a parametric estimation and identification, and state estimation algorithm in the context of discrete-time dynamic systems and with the correct use of technical terminology. D5. Learning skills The student should be able to read and understand reference textbooks on deterministic and stochastic discrete-time dynamic systems, on estimation, systems identification and state estimation.

Calculus basics with specific reference to differential equations and difference equations, complex-variable functions and linear algebra, fundamentals of linear systems theory.

Catalogue of the 6 ECS module “DATA-DRIVEN DIGITAL SYSTEMS” (code 454MI-1) of the integrated course “DATA-DRIVEN DIGITAL SYSTEMS” (code 454MI): 1. Model identification from data: Problem, algorithms, techniques and issues 2. A glimpse on probability theory, random variables and discrete-time stochastic processes 3. Definitions and properties of the estimation and prediction problems 4. Dynamic models of stationary discrete-time stochastic processes: AR, MA, ARMA, ARX, ARMAX models 5. Least-squares estimation 6. Bayes estimation 7. Solution of the prediction problem: the optimal predictor from observed data 8. Identification of discrete-time stochastic models from observed data. Model validation and model structure determination 9. State estimation from observed data. State observers. Kalman filter and extended Kalman filter 10. Computational Tools - Matlab

More on data-based estimation and identification: - T. Soderstrom. P. Stoica. “System Identification”. Prentice Hall, 1989. - L. Ljung. “System Identification – Theory for the User”. Prentice Hall, 1999. S. Bittanti. “Model identification and data analysis”. John Wiley & Sons, 2019. Also, two textbooks (in Italian) are available: - S. Bittanti. “Identificazione dei Modelli e Controllo Adattativo”. Pitagora Editrice, Bologna 1992, terza edizione 1997 (in Italian) - S. Bittanti. "Teoria della predizione e del filtraggio". Pitagora Editrice, quinta edizione 2000 (in Italian) A few collections of solved exercises: - S. Bittanti, M.Campi. “Raccolta di Problemi di Identificazione, Filtraggio, Controllo Predittivo”, Pitagora Editrice, Bologna 1996 (in Italian) J. Schoukens, R. Pintelon, and Y. Rolain, “Mastering System Identification in 100 Exercises”, 2012, IEEE Press Books are available in the library and on the Internet.

Catalogue of the 6 ECS module “DATA-DRIVEN DIGITAL SYSTEMS” (code 454MI-1) of the integrated course “DATA-DRIVEN DIGITAL SYSTEMS” (code 454MI): 1. Model identification from data Problem, algorithms, techniques and issues. Mathematical models in Engineering and Science; Estimation and prediction from measurements: mathematical models with focus on prediction or control. Preprocessing of available data 2. A glimpse on probability theory, random variables and discrete-time stochastic processes Main definitions and tools: stationarity, average, covariance and correlation, power spectral density. White processes. 3. Definitions and properties of the estimation and prediction problems Theoretical analysis and properties of estimators: biased estimation, minimum variance estimator, asymptotic distribution, convergence in probability, almost sure convergence, level of confidence 4. Dynamic models of stationary discrete-time stochastic processes AR, MA, ARMA, ARX, ARMAX models. Correlation and spectral analysis. Canonical spectral factorization. 5. Least-squares estimation Solution of the linear regression problem. Geometrical interpretation. Probabilistic properties: bias, variance, asymptotic characteristics of the estimate 6. Bayes estimation General concepts, optimal Bayes estimation, comparison with linear estimation, recursive Bayes estimation. Geometrical interpretations. 7. Solution of the prediction problem A glimpse on the theory of optimal prediction. Determination of the optimal predictor from observed data. AR, ARX, ARMA, MA models for prediction. 8. Identification of discrete-time stochastic models from observed data. Linear identification techniques by minimizing prediction error, batch and recursive least square estimation algorithms, adaptive identification. Model validation and model structure determination (Cross-validation, AIC, MDL criteria). 9. State estimation from observed data. Generalities. A glimpse on reachability and observability properties, and on realization methods. State observers. Kalman filter 10. Computational Tools Introduction to Matlab and to the use of live scripts for the analysis of stochastic dynamic systems, for estimation and identification techniques, and for data analysis.

A "partial flipped teaching"; approach is followed, namely asking the students to look in advance at the methodological material made available and dealt with in the specific lecture. During the lectures, "hands-on" exercises using Matlab live-scripts are also proposed and discussed in an interactive way during the lectures (to encourage an active engagement of the students). In addition, further live-scripts are made available as stand-alone exercises, so that students can apply and fully understand the concepts and the computational tools illustrated during the lectures, via hands-on experimentation through guided examples. On the Microsoft Teams platform on which all students are automatically enrolled by the education administration of the University, the slides used in the lectures are made available in advance in a printable form for the students’ convenience in order to enhance the concept transfer during lectures. On Microsoft Teams, the live scripts of the guided examples are made available as well.

The objective of the integrated course is to provide to the students the advanced methodological tools for the analysis of dynamic systems in the discrete-time domain both in a deterministic (the 3 ECS module “DIGITAL SYSTEMS”, code 454MI-2) and in a stochastic setting (the present 6 ECS module “DATA-DRIVEN DIGITAL SYSTEMS” code 454MI-1). Specifically, the present module deals with the analysis and design of estimation, prediction and identification algorithms using experimental data, and with the design and implementation of state estimation algorithms in a deterministic and in a stochastic framework. As a whole, the integrated course 454MI made of 454MI-1 and 454MI-2 is designed as a complement of the course of Fundamentals of Automatic Control offered at the second year of the degree courses since it is focused on the discrete-time context which is more suitable to address topics in ICT and data management. The course extends the knowledge base towards estimation and identification techniques from experimental data and addresses the practical implementation aspects. The course is suitable for 4th year students both in the industrial context and in the ICT and data management framework. The present 6 ECS module is the second within the logical flow of the entire integrated course with code 454MI. The topics deals with focus on stochastic discrete-time systems, with emphasis on estimation and identification methodologies using experimental data.

Partial Tests For the entire integrated course, three partial tests are carried out to evaluate the competences acquired by the students enrolled in the course. “TEST A” is carried out during the 3 ECS module 454MI-2 and “TEST B” and “TEST C” are carried out during the 6 ECS module 454MI-1. Only students attending the course for the first time in A.A. 2025-2026 are admitted to the partial tests in the A.A. 2025-2026. Each test consists in the solution of specific problems via the creation of Matlab code and, when required, an explanation of the solution method. The tests have an open-book format and are carried out by the students during the course timetable in a room provided with computers. For the 3 ECS module 454MI-2, “TEST A” has a duration of 1 hour, is carried out in the “Matlab Online” platform, and focuses on topics 1-4 (of 454MI-2). The evaluation of TEST A, together with the evaluation of TEST B and C of the 6 ECS module 454MI-1 for students taking the 9 ECS entire 454MI course) contribute to the final marks according to the following rules: If final cumulative mark Ptot of the three intermediate tests is greater than or equal to 18/30, the following options are available at the student discretion: Option 1: Agreed in Esse3 on the final mark Ptot Option 2: Carry out an additional (open book) partial written examination with a duration of 1 hour and with a maximum additional mark to Ptot equal to 5/30. The registration of the cumulative mark is at the student discretion. Option 3: Carry out the full examination described in the following. Expiration: using the partial tests cumulative mark Ptot is allowed during the current academic year (for the academic year 2025/2026 until the end of the examination session in February 2027). When the exam sessions of the current academic year are over, the cumulative mark Ptot expires. Full Exam The full exam is strictly personal, group work is not allowed, and it refers to the 9 ECS 454MI course. The exam is made of Parts 1, 2, and 3 aimed at evaluating the competences acquired by the students enrolled in 454MI course. Each part consists in the solution of specific problems via the creation of Matlab code and, when required, an explanation of the solution method. The three parts have an open-book format and are carried on dates selected in advance during the academic year in a room provided with computers and specific software. Part 1 has a duration of 1 hour, is carried out in the “Matlab Online” platform and focuses on the same topics of partial TEST A. Part 2 has a duration of 1 hour, is carried out in the “Matlab Online” platform and focuses on the same topics of partial TEST B. Part 3 has a duration of 1 hour, is carried out in the “Matlab Online” platform and focuses on the same topics of partial TEST C. Part 1, 2, and 3 evaluations contribute to the final marks according to the following rules: If final cumulative mark Ptot of Part 1, 2, and 3 is greater than or equal to 18/30, the following options are available at student discretion: Option 1: Agree in Esse3 on the final mark Ptot. Option 2: Carry out an additional oral examination just after Parts 1, 2, and 3 with a duration of 1 hour and with a maximum additional mark of 5/30. The student is asked to answer questions to evaluate their communication skills and knowledge and understanding. The questions are related to all possible topics that were discussed and analysed during lectures. Also, a short discussion about the content of the submitted Parts 1, 2, and 3 could take place. If Ptot (with or without the additional oral examination) is greater than 30/30 the registered mark is 30/30 with honors. The registration in Esse3 of the cumulative mark of Ptot and the oral examination is at the student discretion.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)