Lectures related to Networked Control Systems: Laplacian Operators and Microgrids

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

Laplacian Matrix: Properties and Examples

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

Covers the concept of the exponential family and discusses forward and backward maps, expensive computations, parameters, functions, and convexity.

Laplacian Matrix in Networked Control Systems

Explores the Laplacian matrix in electric and mechanical networks, consensus, and properties of Laplacian matrices in networked control systems.

Graph Algorithms: Modeling and Traversal

Covers graph algorithms, modeling relationships between objects, and traversal techniques like BFS and DFS.

Graph Theory: Connectivity and Properties

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

Networked Control Systems: Coordination Among Agents

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

Networked Control Systems: Laplacian Matrix and Consensus

Explores the Laplacian matrix and consensus in networked control systems.

Sparsest Cut and Concurrent Flow

Covers sparsest cut, NP-completeness, Bougains Theorem, and concurrent flow in graphs.

Statistical Analysis of Network Data: Structures and Models

Explores statistical analysis of network data, covering graph structures, models, statistics, and sampling methods.

Filters Fundamentals: Chebyshev Approximation

Explores the fundamentals of Chebyshev approximation in filters, covering polynomials, pole locations, order determination, and design procedures.

Graph Theory Fundamentals

Explores fundamental graph theory concepts, Erdős' results, Chromatic Lemma, and Union Bound theorem in graph theory.

Fixed Points in Graph Theory

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Graph Theory Fundamentals

Covers the fundamentals of graph theory, including vertices, edges, degrees, walks, connected graphs, cycles, and trees, with a focus on the number of edges in a tree.

Consensus Algorithms: Weight Assignment and Applications

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

Networked Control Systems: Laplacian Flow and Heat Equation

Explores Laplacian flow, heat equation analogies, and microgrid networked controllers.

Filters Fundamentals: Chebyshev Polynomials and Filter Design

Covers Chebyshev polynomials, all-pole filter design, RLC filters, and active-RC and OTA-C filter implementations.

Shortest Path Algorithms: BFS and Dijkstra

Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.

Networked Control Systems: Microgrid Controllers and Cybersecurity

Covers microgrid controllers, cybersecurity, consensus-based control, and cybersecurity vulnerabilities in networked control systems.

Networked Control Systems: Opportunities

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