Lecture
This lecture covers the balancing of directed graphs, analogies between the Laplacian flow and the heat equation, and a case study on networked controllers for microgrids. It delves into Laplacian matrices, consensus theorems, Laplacian operators, and Laplacian flow for undirected connected graphs. The instructor explains the design of balanced digraphs, Laplacian operators in calculus and on graphs, and the Laplacian matrix as a diffusion operator. The lecture also explores microgrids, their overview, hierarchical control, and the flexibility and scalability of control systems, emphasizing the key role of graph Laplacians in analyzing consensus algorithms and physical models.