Lectures related to Networked Control Systems: Strongly Connected Components and Condensation Digraphs

Topological Sort and SCC

Explores topological sort, acyclic graphs, Strongly Connected Components, magic algorithm, component graph, flow networks, and their applications.

DFS Continuation: Topological Sort

Covers topics like DFS output, edge classification, acyclic graphs, correctness, time analysis, SCCs, and the Topological Sort algorithm.

Networked Control Systems: Consensus Algorithms in Digraphs

Explores consensus algorithms in digraphs, focusing on scenarios where the digraph is not strongly connected.

Graph Sketching: Connected Components

Covers graph sketching and connected components in streaming models.

Networked Control Systems: Convergence Rate and Digraphs

Explores convergence rate in networked control systems and consensus in digraphs, emphasizing the challenges of computing Pess(A) and weight assignment.

Connectivity in Graph Theory

Covers the fundamentals of connectivity in graph theory, including paths, cycles, and spanning trees.

Networked Control Systems: Coordination Among Agents

Explores coordination among agents in networked control systems through graph theory and real-world examples.

Laplacian Matrix: Properties and Examples

Explores the Laplacian matrix, time-varying consensus theorems, and balanced graphs in networked control systems.

Networked Control Systems: Properties and Connectivity

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

Graph Theory: Connectivity and Properties

Explores the properties of undirected and directed graphs, emphasizing connectivity and network topology modeling.

Algebraic Graph Theory: Matrices and Connectivity

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

Flow Networks: Strongly Connected Components

Introduces Strongly Connected Components and Flow Networks, discussing algorithms and applications.

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

Discusses the Ford-Fulkerson method and strongly connected components in graph algorithms.

Networks: Paths and Components

Explores simple paths, connectivity, equivalence classes, and connected components in directed graphs.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Networked Control Systems: Opportunities

Explores coordination in networked control systems, graph theory, and consensus algorithms.

Consensus Theorem for Communication Networks

Explores the consensus theorem for communication networks and the implications of various consensus properties in networked control systems.

Networked Control Systems: Laplacian Operators and Microgrids

Explores Laplacian operators on graphs and the model of DC microgrids.

Networked Control Systems: Consensus and Laplacian Flow

Explores the Laplacian flow and achieving consensus in networked control systems through examples and theorems.

Consensus Algorithms: Weight Assignment and Applications

Explores the design of graph weights for consensus and applications in sensor networks.