# teaching

Networked Dynamic Systems AA 597 (Spring 2022 @ UW)

**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) |
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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 |