Extra credit opportunities

A typical offering of this course has had few extra credit opportunities. The last time I taught it, I offered extra credit for scribing the lecture notes. My hope was that we could augment the transcribed set with quality transcriptions that could be added to the course website (similar to the initial set of notes provided for the first few weeks) – it didn’t really work out as there was no way to perform quality control.

So this time, I have slightly changed the scribing requirements while also providing a different way to earn extra credits. Students must choose one of the following methods.

Note

Doing either of these is completely optional – simply acing the homework and the exams should be sufficient to earn an \(A\) in this course.

1. Optional scribing

Students enrolled in the course have the opportunity (on a first-come first-served basis) to transcribe the lectures into lecture notes to be shared with the class.

Each quality transcription (see first few for examples on the Lectures page) can earn up to 2% extra credit in the course (to make up for points lost in the midterms, homework or final exam) for a maximum of up to 8%.

Sign up here to scribe the lectures (limited to two students per lecture). Transcribed notes must be submitted as .qmd files within two weeks of the corresponding lecture.

To see examples of Quarto Markdown files, click the </> Code button at the top of the currently transcribed lecture notes. To see how your Quarto files might display on this website, see the source code for the course website and instructions therein (as of the first day of instruction).

2. Optional project

ECE 515 (also ME 540 & SE 522) has always been a theory course. The content we cover is mathematically beautiful and truly builds the fundamentals required to delve deeper into modern control theory. Traditionally, there has been nary a computational project in 515. I took the course in this traditional format many many years ago, and I intend to, for the most part, hew to tradition.

That said, these days reinforcement learning, deep learning and AI, and all that is the rage – so I thought, naively maybe (remains to be seen):

“How can we use something like ChatGPT to make 515 more interesting?”.

Your extra credit project, if you choose to do it – again, it is absolutely unnecessary to do this project to get an \(A\) in this course – will be to build an applet/webpage/interactive demonstration of some concept we study in ECE 515 while being free to use Generative AI.

Here is an example I built.

If you choose to go this route you can recieve upto 8% extra credit.

  • 1% for a proposal (due by the end of Week 5, October 17)
  • 7% for a working prototype (due by last day of instructions) composed as follows:
    • 1% for a publicly accessible, well documented (e.g. has README.md file) Github repository
    • 2% if the TA is able to follow your instructions and get your demonstration running
    • 2% for correct technical analysis of topic and interpretation of results/demos
    • 2% for accompanying explanatory write-up of the content of notebook/demo.

Possible topics

Below is a non-exhaustive and unverified list I put together glancing over our class notes.

Warning

Some of the suggestions below may not be feasible in a three-week span, may be computationally prohibitive or may not be solvable at all.

Chapter 1 - Modeling and analysis

  • Pick a harder system like the Furuta pendulum, or an airplane, etc. and do something similar to this notebook (PID, LQR, some feedback control). Demonstration should have some interactivity.
  • Create an applet that given \(\dot x = f(x)\) where \(x \in \mathbb{R}^n\) (user provides \(f(x)\)) visualizes 2D sections (user picks which) of the phase space.

Chapter 2 - Linear algebra

  • Create demonstrations or visualizations of finite dimensional linear operators. Visualize the various interpretations of determinants in two and three dimensions. What about higher dimensions?
  • Show (i.e. demonstrate interactively) applications of eigenvalues (e.g. eigenfaces, vibrations, musical instruments, etc.) in a notebook.

Chapter 3 - Solutions to state equations

  • Examine approximations to LTV solutions using the Peano-Baker series – how drastically do the solutions change as more and more terms are added? Visualize in an interactive notebook.
  • Create a notebook that computes the Lyapunov-Floquet transformation of an LTV system (say 2x2 or 3x3). Find a way to visualize the time varying change of coordinates.
  • Read about Carlemann linearization (Wikipedia is woefully inadequate) – evaluate the effectiveness of different orders of Carleman linearization at various points in the phase space of a Van der Pol oscillator.

Chapter 4 - Stability

  • Create a tool that verifies whether a given (polynomial) function is a Lyapunov function or not for an autonomous system. If not, report what is violated.
  • Read about Center manifold theorem(s) and create a nice notebook explaining it with visuals for a few non-trivial examples. Make it interactive.

Chapters > 5

  • Create an interactive notebook that can generate realizations of relatively manageable MIMO transfer functions (see Section 6.6 in the Class Notes)
  • More TBD by end of Septemeber