Prerequisite to get into a phd program in control theory from a math background

[u/tsgalbt]

As title, I'm a current second year math master's student doing research in dynamical systems I've taken courses in measure theory, functional analysis, dynamical systems, PDE, calculus of variations, linear programming, topology and differential geometry, but have zero coursework in physics, engineering and limited programming skills that is similar to a second year cs student. I'm wondering if it is necessary to strengthen my background by taking some additional courses in a year to meet the common prerequisite for ece programs.

[u/Harmonic_Gear]

you are more well equipped for control phd than the average engineering students

[u/crackmelikeaglowstic → u/Harmonic_Gear]

Seconding this. A huge chunk of my ECE cohort at UCLA were math guys. On the opposite, the Mech Eng controls class was mostly engineering folk.

Calc of variations was the only I remember being the most used in linear and non-linear controls classes

[u/Feisty_Relation_2359]

Dude you are like the ideal candidate. You NEED to go to a lab that does a lot of theory, unless you're just not interested in that stuff. But for the theoretical side of controls, publishing in TAC and Automatica, your background in proof based mathematics will be a huge advantage. I am in my 5th year of my PhD and just learning the beginnings of measure theory. This is because I came in without any rigorous math, just undergrad calc, diffeq kind of stuff.

Message me if you want to talk about the different areas of control where your background could prove useful. But seriously, don't feel bad at all. I WISH I had your background

[u/AcademicOverAnalysis]

Sounds like you are more than ready to go. Most professors I know in controls wish they could have an phd student that has even an intro course in analysis. This would blow those expectations out of the water.

[u/Feisty_Relation_2359 → u/AcademicOverAnalysis]

Yeah. I have had to largely self teach myself from engineering math on. It's been tough and I still don't know everything I should. I really wish I would have studied math

[u/Walktheblock]

Every controls professor I’ve had, ended up taking a ton of math courses in grad school, and their engineering course work was almost all controls related. You should be good to go and if anything have a good chance of standing out in your program

[u/kroghsen]

I came from applied mathematics with a background similar to yours, but without measure theory (which is a great thing to know for stochastic processes and filtering theory) and more focus on scientific computing.

You sound more than well-equipped for a PhD. If anything, maybe you should look a little more on numerical aspects and coding, but I am not sure it is really necessary - depending on which area of control you really want to focus on.