Networks are pervasive across all levels of the organizational structure of matter, ranging from the microscopic scale of atoms and molecules to the macroscopic realms of the World Wide Web, ecological systems, and global supply chains. The advent of the digital revolution has facilitated connections among individuals, organizations, and communities on a global scale, effectively transforming the world into a huge network. The traditional architectures of control systems, consisting of a plant, a controller, actuators, and sensors, are giving way to networked control systems. In these systems, the functions of decision making, data processing, sensing, and actuation are distributed among simpler subsystems that are referred to as agents and can be separated by large distances. The agents are capable of cooperating with each other to achieve their goals and, at the same time, might be autonomous in their decision making and need not be controlled from a single center. Understanding the principles of networked control systems' functioning is vital for modern system engineering, particularly in the development of Internet of Things (IoT), smart infrastructures, automated factories, algorithms for coordinated motion of connected vehicles and robots. Many algorithms for networked control are inspired by dynamics observed in human societies and animal populations, e.g., fish schools or bird flocks. Networked control is also closely related to dynamics of epidemics and their containment. The goal of this course is to introduce basic concepts of dynamical networks, their structural properties (elements of graph theory) and some control algorithms (e.g., consensus and synchronization), as well as several simple models of networks inspired by social and natural sciences.

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. Desirable, yet not strict prerequisites, are: basics of differential equations, linear control theory, basic of probability, convex functions.

Main topics of this course are: -- basics of graph theory, graphs' connectivity types, Laplacian matrix, algebraic connectivity; -- basics of probability (discrete distributions and densities); -- statistical models describing real-world large graphs (Watts-Strogatz small-world networks, Erdos-Renyi random graphs, scale-free networks); -- linear and nonlinear state-space models, eigenvalues, local stability and stabilization (LQR, pole placement); -- Lyapunov functions and criteria for stability in large; -- multi-agent consensus and its applications (opinion dynamics modelling, formation control, coupled oscillators); -- controlled synchronization of general dynamical systems, pinning control of networks; -- applications to distributed convex optimization, optimal distributed estimation and load balancing; -- networked models of epidemics and algorithms for their containment.

The course consists of theoretical material (including examples and exercises) and laboratory practicums and organized into three modules: 1. Introductory module: -- graph theory; -- basics of probability; -- basics of Matlab, solving continuous-time and discrete-time equations. -- Introduction to state-space models, stability and stabilization. -- Laboratories on Matlab and graph visualization. 2. Collective behaviors in dynamical networks: self-organization and control. -- 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 optimization. -- Laboratories on consensus and synchronization. 3. Dynamics and control of epidemics (seminar-laboratory). 4. Project on modeling of a dynamical network and/or group of cooperating agents (performed in groups, final report is discussed as a part of exam).

The recommended books: 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

Slides; Esercizi; Esercitazioni di laboratorio;

Modalità di esame: Test informatizzato in laboratorio; Elaborato progettuale in gruppo;

Exam: Computer lab-based test; Group project;

... The exam consists of two parts: 1) Computer-based Quiz with multiple-choice and open questions (students should bring their computers), the maximal mark is 16 points. 2) Group project activity is assigned during the semester in order to check the ability of the students to apply the tools and results presented in the lectures. The maximal mark is 15 points. Participance in both parts is mandatory, the student should collect at least 8 points for the Quiz and 18 points in total to pass.

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.