Dynamics and Control of Networks
Code  Completion  Credits  Range  Language 

BE3M35DRS  Z,ZK  6  2P+2C  English 
 Lecturer:
 Kristian HengsterMovric
 Tutor:
 Kristian HengsterMovric, Štefan Knotek
 Supervisor:
 Department of Control Engineering
 Synopsis:

The course offers a response to the increasing demand for understanding of networks  largescale and complex dynamical systems that are created by interconnecting components and subsystems. We will not restrict ourselves to one physical or technological domain. Quite the opposite, we will analyze the networkrelated phenomena found in several domains, including societal, economic, or biological. We will analyze the fundamental similarities among flight control of formations of unmanned aerial vehicles, tigh distance regulation in platoons of trucks on highways, generation and distribution of energy in smart grids, realization of a phone call in a cellular phone network, manipulation of a community through Facebook, or even forecasting the epidemics spread over a globe. For such networks, the resulting behavior is given not only by the individual components and subsystems but also by the way in which they are interconnected (topology of the network). Understanding these issues goes far beyond the boundaries of individual physical and technological or scientific domains.
In the first part of the course we will introduce fundamental theoretical and computational concepts for analysis of networks, in particular, we will introduce basics of algebraic graph theory and network algorithms. In the second half of the course we will view the network as a dynamic system and we will study its properties and the ways in which these properties can be affected (controlled). We will use the methodologies from the automatic control theory. Finally, we will introduce some interesting tools for analysis and synthesis of networked systems such as wave and scattering description and distributed optimization.
 Requirements:
 Syllabus of lectures:

1. Basic concepts and examples of technological, information, social and biological networks.
2. Algebraic and spectral graph theory: graph Laplacian, incidence matrix, adjacency matrix, incidence matrix, degree, eigenvalues and eigenvectors, irreducible and balanced graph, rigid graph.
3. Algorithms for analysis of largescale networks  PageRank, centrality, clusters.
4. Type of graphs and networks: random graph, smallworld network, regular graph, scalefree network.
5. Social and biological networks, leaders, complexity.
6. Resilience of network and epidemics on networks.
7. Dynamics in networks.
8. Consensus (agreement) in networks, synchronization (for example in smart grids), internal model principle.
9. Formation control: controllability and observability in a graph, stability of formation.
10. Distributed control of distributed systems: stability, performance, passivitybased control.
11. Distributed estimation (for example, in wireless sensor networks).
12. Scaling phenomena in distributed control of distributed systems. : string instability, coherence.
13. Wave and scattering methods for modeling, analysis and synthesis of networked systems.
14. Distributed optimization: Alternating directions method of multipliers (ADMM), subgradient methods.
 Syllabus of tutorials:

The exercises will be dedicated to solving some computational problems together with the instructor and other students.
 Study Objective:

Get familiar with the computational frameworks for analysis and synthesis of largescale complex interconnected systems ? networks.
 Study materials:

These are the books on which the course has been built. Students will be expected to used them during the course (a number of copies will be bought into the library):
[1.] Mark Newman. Networks: An introduction. Oxford University Press, 2010, ISBN: 9780199206650.
[2.] Mehran Mesbahi and Magnus Egerstedt. Graph Theoretic Methods in Multiagent Networks, Princeton University Press, 2010, ISBN: 9780691140612
 Note:
 Further information:
 https://moodle.fel.cvut.cz/courses/BE3M35DRS
 Timetable for winter semester 2021/2022:
 Timetable is not available yet
 Timetable for summer semester 2021/2022:
 Timetable is not available yet
 The course is a part of the following study plans:

 Cybernetics and Robotics (compulsory elective course)