# Is there any application of control engineering to the study of algorithms stability or computer science theory?

I am an undergraduate student in Electrical and Computer engineering. In our 5th semester we have a obligatory "Introduction to control systems course". I was wondering if these bunch of math theories is applicable to other directions of my school rather than the obvious (in the next semester we choose majors and there is one called signals and automation which basically involves every "advanced" control theory module, but I want to know if it is useful other than that).
I like the ideas of the course, but I am not really into the hardcore applications of it. I think I want to follow a more theoretical path which involves math applicable to computer science. So if I do not go for the "automation and signals major" but into computer science, hardware and math major, is there any chance I find it useful? For example because it involves the stability, I have seen some advanced graduate seminars where people talk about the convergence of algorithms ...maybe some control theory theorems are useful there?

• Most of these have been studied and worked on because they are useful. If you want things that are not useful (yet) then consider Pure Mathematics. – Solar Mike Nov 21 '20 at 17:22

## 2 Answers

Basic control theory is very useful in a wide range of situations. Really advanced control theory is specialized and useful to theory and complex design of certain actual control systems.

I had math in grad school, and EE undergrad, worked as a Systems Engineer. I had control theory in both undergrad and grad school. I do not see any use for control theory in convergence of algorithms or in a setting of math theorems.

That said you may find an application and become a star in a new math field.

Possibly this is a slightly old question...

An "introduction to control theory" course sounds unlikely to cover this stuff, but one of the control courses in the Masters' year I'm in right now includes topics that might be of interest to you:

• Convex optimisation
• Semi-definite programming to guarantee stability
• Distributed algorithms (most importantly proximal algorithms)
• Scenario approach to make probabilistic guarantees

We don't ever study the implementation of any solvers, but this whole course is basically on convergence and stability and draws on quite a lot of areas. Helly's theorem was a bit of highlight!

This book talks about the interpretation of the ADMM algorithm as integral control of a dynamical system in chapter 4: https://web.stanford.edu/~boyd/papers/pdf/prox_algs.pdf

The nyquist criterion will likely be included in the introductory course which does draw on results like Cauchy's argument principle, which is some fairly abstract maths too, but you'll probably need to do your own reading for the details. Sutdy of dynamical systems relies a lot on results from topology: the "hairy ball theorem" makes me laugh every time. Most things are applicable to other things in engineering though it seems! Control theory seems like a great place to start for computer science to me, but fred probably does know better, I am a lowly undergraduate too!

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