At the end of the course, the student will know the main paradigms of networked control systems design, describe and predict behaviors of dynamical networks. More specifically, students learn -- modeling of networks and dynamical networked systems in Matlab; -- basics of graphs theory, probability and state-space dynamical models; -- main distributed algorithms to control cooperating autonomous agents and benchmark problems (consensus, synchronization); -- networked models arising in social and natural sciences (opinion dynamics, coupled oscillators, flocks, dynamics of epidemics); -- applications in engineering (distributed optimization, platoons of vehicles, control of mobile robots, estimation in sensor networks).

Strict prerequisites for this course are limited to 1) basics of higher algebra - operations on vectors and matrices, complex numbers, eigenvalues; 2) basics of calculus (mathematical analysis) - derivative, partial derivatives, gradients, Jacobian matrix, integral, minimization of scalar functions and differential equations. Desirable, yet not strict prerequisites, are: 3) linear control theory in time domain (stability, controllability, observability) and frequency domain (transfer functions) 4) basic of probability theory.

The course consists of theoretical material (including examples and exercises) and laboratory practicums and organized into three modules: 1. Introductory module (20h of lectures + 6h of labs): -- Graph theory; -- Basics of Matlab, solving continuous-time and discrete-time equations. -- Recollections state-space models, stability and stabilization. 2. Collective behaviors in dynamical networks: self-organization and control (30h lectures+10h labs) -- Consensus, self-synchronization and controlled synchronization in networks; -- Applications to control of vehicles and mobile robots; -- Networked models in natural and social sciences (opinion dynamics, oscillators, flocks etc.); -- Applications to distributed estimation and computing. 3. Models of epidemics (10h of lectures +4h of labs). Optional: Project on modeling of a dynamical network and/or group of cooperating agents (group activity, final report is discussed as a part of exam) . The introduction of the project takes 1h of lectures.

The course consists of lectures, laboratory practicums and the seminar-lab on epidemics modelling. 60 hours of lectures cover: -- the theoretical topics of the course (basics of graph theory, state-space dynamical models, analysis and control of multi-agent systems and dynamical processes over networks); -- some numerical examples and solved problems; 20 hours of laboratories aim at enabling students to use MATLAB and Simulink software for numerical simulation, rigorous analysis and design of networked control systems and dynamical processes over graphs. The topics of exercises are: -- basics of Matlab, vectors and matrices, solving of differential and difference equations, plotting functions; -- basics of graph theory, modelling and visualization of random graphs; -- multi-agent consensus, simple models of opinion formation and flocking; -- controlled synchronization, LQR design of distributed controllers; -- lab-seminar on modeling and control of epidemics.

The recommended books and papers: 1) F. Bullo, Lectures on Network Systems, downloadable at https://fbullo.github.io/lns/ 2) D. Easley and J. Kleinberg, Networks, Crowds, and Markets: Reasoning About a Highly Connected World, can be downloaded at https://www.cs.cornell.edu/home/kleinber/networks-book/networks-book.pdf 3) A.L. Barabási, Network Science, can be read online at http://networksciencebook.com/ 3) G. Notarstefano, I. Notarnicola, A. Camisa, Distributed Optimization for Smart Cyber-Physical Networks, Foundations and Trends in Systems and Control, 2019 4) Lewis, F.L., Zhang, H., Hengster-Movric, K., Das, A., Springer, Cooperative Control of Multi-Agent Systems, 2014 5) W. Mei et al., On the dynamics of deterministic epidemic propagation over networks//Annual Reviews in Control Volume 44, 2017, Pages 116-128

Lecture slides; Exercises; Lab exercises;

Exam: Group project; Computer-based written test in class using POLITO platform;

Students can choose between two exam options: (a) Quiz Only (b) Quiz + Project QUIZ DETAILS 1) Format: The mandatory computer-based quiz is conducted in the computer lab (LAIB) and consists of 8 problems, which may be multiple-choice or open-ended. Some problems require Matlab for solution, a hands-on practicum will be provided as part of the laboratory exercises. 2) Scoring: Each problem is worth 4 points if fully solved. Partial credit is available for open-ended questions. Wrong answers are not penalized. 3) Duration: The quiz lasts 2 hours. 4) Restrictions: Students must not use their own computers or any electronic devices. Use of written or printed materials, such as books, lecture notes, or printed Matlab scripts, is also strictly prohibited. Students with special needs are kindly asked to contact the examiners in due time to arrange for the formula sheet (il formulario). PROJECT DETAILS [OPTIONAL] 1) Proposal: The projects are proposed in the 5th or 6th week of the course and are typically undertaken by groups of 3-4 students. 2) Content: Each project involves reading a research paper and conducting a numerical simulation of a networked system (e.g., modeling 3) epidemic spread or opinion formation in a social network). 3) Submission: Groups must submit a brief report (no more than 10 pages) by a specified deadline and give a 20-minute presentation at the end of the semester. 4) Scoring: The project is worth a maximum of 10 points, with up to 5 points for the presentation and up to 5 points for the report. FINAL MARK: (a) If a student prefers the Quiz Only option, their final grade is solely based on the quiz score. A perfect score of 32 points is registered as 30 e lode. The minimum passing score for the quiz is 18 points. (b) The option Quiz + Project is available only to students participating in the optional projects. The final grade is the sum of the quiz and project scores, capped at 31 points (=30 e lode). However, the minimum passing score for the quiz in this option is 12 points. Students scoring below 12 must retake the quiz.

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.