A networked dynamic system is a set of dynamical units that interact over a signal exchange network for its coordinated operation and behavior. Such systems have found many applications in diverse areas of science and engineering, including multiple space, air, land, and underwater vehicles, energy and power systems, physiology, and medicine. Currently, there is an active research effort underway in control and systems community to formalize these dynamical systems and lay out a foundation for their analysis and control synthesis. This course provides an overview of graph-theoretic techniques that have proven instrumental for studying networked dynamic systems.

Class Time: (M/W) 11:30 pm - 12:50 pm

Class websites: Canvas page (homework submissions) and https://shahriarta.github.io/teaching/

Class Room: GUG 204/ Zoom Link

Office Hours: Wednesdays 2:00-3:00 pm in Zoom Link/GUG 305 (Shahriar);
Fridays 3:30-4:30 pm in Zoom Link (Dan);
We can always setup up another time by email too.

You can find the syllabus here.

You can also access an online copy of the main textbook here, provided by the UW library.

Also see another great textbook here.

Homework:

Here is the first homework assignment PDF (Due April 22, 2022).

Here is the second homework assignment Jupyter notebook (Due May 8, 2022). Here is short tutorial how to setup and use Jupyter Notebooks.

Course Schedule (Tentative)

Date Topic Resources Prerequisite Extra resources
March 28th syllabus/logistics + intro Chp 1 and 2 [Mesbahi2010Graph]; Algebraic Graph Theory Slides Linear Algebra [Horn2013Matrix]: left/right nullspace, rank-nullity theorem, Singular-value Decomposition (SVD), Moore–Penrose psuedo-inverse Superspreaders of Covid-19; Controllability of brain network;
March 30th Introduction to algebraic graph theory Algebraic Graph Theory Slides (updated) Linear Algebra [Horn2013Matrix]: Positive semi-definite (PSD) matrices, Eigen-value Decomposition (EVD)
Apr 4th Laplacian, its spectrum and connectivity Chp 2 [Mesbahi2010Graph], Algebraic Graph Theory Slides (annotated) Linear Algebra: same circulant matrices
Apr 6th Agreemment protocol (undirected graph) Chp 2 and 3 [Mesbahi2010Graph], Notes (AP) Linear systems: Basic linear dynamical systems, their solution, stability and convergence properties
Apr 11th Agreemment protocol (directed graph + discrete time) Chp 3 [Mesbahi2010Graph], Notes (directed AP) Linear systems: same; Linear algebra [Horn2013Matrix]: non-negative matrices and their properties
Apr 13th Agreemment protocol (directed graph + discrete time) Cont. Chp 3 [Mesbahi2010Graph], Notes (directed AP-cont.) Linear systems: same; Linear algebra [Horn2013Matrix]: non-negative matrices and their properties, Perron–Frobenius theorem
Apr 18th Factorization Lemma Cont. Chp 3 [Mesbahi2010Graph], Notes (Factorization Lemma) Linear systems: same; Linear algebra [Horn2013Matrix]: Kronecker product of matrices
Apr 20th Varying graph Chp 4 [Mesbahi2010Graph] Notes (Lyapunov methods) Linear systems: same; Linear algebra [Horn2013Matrix]: Perron–Frobenius theorem, [Mesbahi2010Graph, Appendix]: Lyapunov stability, LaSalle's invariance principle
Apr 25th Varying graph (cont.)+ Edge consensus Chp 4 [Mesbahi2010Graph] Notes (Lyapunov methods cont.+ Edge consensus) Linear systems, Linear algebra, [Mesbahi2010Graph, Appendix]: LaSalle's invariance principle for switched linear systems Block Matrix Multiplication, and Eigenvalue-Eigenvector
Apr 27th discretization and generalization of A.P. Chp 4 [Mesbahi2010Graph] Notes (discretization vs discrete sampling) Linear systems: same; Linear algebra [Horn2013Matrix]: Perron–Frobenius theorem, Metzler matrices Moreau'04, and Moreau'05; time-varying graph
May 2nd Discrete A.P. and distributed estimation Chp 8 [Mesbahi2010Graph] Notes Discrete linear systems: Linear algebra [Horn2013Matrix]: Perron–Frobenius theorem, irreducible and primitive matrices Metropolis weights; Consensus on opinions
May 4th Distributed Kalman Filtering Chp 8 [Mesbahi2010Graph] Notes and Slides Discrete linear systems; Linear algebra [Horn2013Matrix]; Kalman Filter Python slides (Numpy array)
May 9th Kalman Filtering (cont.)+ distributed optimization Chp 8 [Mesbahi2010Graph] Kalman Filter2 Discrete linear systems; Linear algebra [Horn2013Matrix]; Kalman Filter Distributed Dual Averaging
May 11th distributed optimization (Cont.) notes Discrete linear systems; Linear algebra [Horn2013Matrix]; Basic convex analysis Distributed Dual Averaging
May 16th distributed optimization (Cont.) + Formation Control Chp 6 [Mesbahi2010Graph], notes Discrete linear systems; Linear algebra [Horn2013Matrix]; Basic convex analysis
May 18th Formation Control (Cont.) Chp 6 [Mesbahi2010Graph], notes Discrete linear systems; Linear algebra [Horn2013Matrix];
May 23th Controllability of Networks Chp 10 [Mesbahi2010Graph], notes Controllability and Observability of linear systems; PBH test slides of LMIs for Controllability by M. Peet