**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Networked Control Systems: Consensus Algorithms in Digraphs

Description

This lecture by the instructor covers consensus algorithms in digraphs, focusing on the case where the digraph is not strongly connected. The main result from previous lectures is discussed, emphasizing the consensus algorithm's behavior with primitive and stochastic matrices. The lecture explores scenarios where the digraph is not strongly connected, providing examples like opinion dynamics with a single globally reachable node. The concept of powers of adjacency matrices is introduced, along with discussions on reducible digraphs and induced subgraphs. The lecture concludes with a proof regarding strongly connected components and globally reachable nodes in digraphs.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

In course

Instructor

Related concepts (58)

ME-427: Networked control systems

This course offers an introduction to control systems using communication networks for interfacing sensors, actuators, controllers, and processes. Challenges due to network non-idealities and opportun

Adjacency matrix

In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.

Industrial control system

An industrial control system (ICS) is an electronic control system and associated instrumentation used for industrial process control. Control systems can range in size from a few modular panel-mounted controllers to large interconnected and interactive distributed control systems (DCSs) with many thousands of field connections. Control systems receive data from remote sensors measuring process variables (PVs), compare the collected data with desired setpoints (SPs), and derive command functions that are used to control a process through the final control elements (FCEs), such as control valves.

Adjacency list

In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs. An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges.

Distributed control system

A distributed control system (DCS) is a computerised control system for a process or plant usually with many control loops, in which autonomous controllers are distributed throughout the system, but there is no central operator supervisory control. This is in contrast to systems that use centralized controllers; either discrete controllers located at a central control room or within a central computer. The DCS concept increases reliability and reduces installation costs by localising control functions near the process plant, with remote monitoring and supervision.

Control system

A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The control systems are designed via control engineering process. For continuously modulated control, a feedback controller is used to automatically control a process or operation.

Related lectures (45)

Irreducible Matrices and Strong ConnectivityME-427: Networked control systems

Explores irreducible matrices and strong connectivity in networked control systems, emphasizing the importance of adjacency matrices and graph structures.

Consensus in Networked Control SystemsME-427: Networked control systems

Explores consensus in networked control systems through graph weight design and matrix properties.

Algebraic Graph Theory: Matrices and ConnectivityME-427: Networked control systems

Explores algebraic graph theory applied to networked control systems and consensus algorithms.

Spectral Properties of Non-negative MatricesME-427: Networked control systems

Covers the spectral properties of non-negative matrices and their interpretation in digraphs.

Networked Control Systems: Properties and ConnectivityME-427: Networked control systems

Explores properties of matrices, irreducibility, and graph connectivity in networked control systems.