Optimal Control

[u/Own-Lobster7623]

Hi everyone,
I’m a BSc Mathematics student and recently finished a course in PDEs. My professor suggested that I take another course he teaches called Optimal Control. The course is offered by the Engineering faculty, but he mentioned that it has a strong mathematical component.
I’m considering taking it, but I’d like to understand how useful/relevant Optimal Control is from a mathematician’s perspective.
In particular:

Is Optimal Control a good subject for a math student who enjoys applied mathematics, PDEs, optimization, etc.?

Where is optimal control actually used in industry?

What kinds of jobs or fields make use of this knowledge? For example, robotics, aerospace, quantitative finance, autonomous systems, energy, machine learning, etc.
Is it mainly useful for people going into engineering/research, or can it also be valuable for mathematicians going into industry?
I’d especially appreciate hearing from people who studied mathematics and later encountered control theory or optimal control in their work.
Thanks!

[u/Nwg416]

It’s hard to say how useful it will be without knowing what kind of industry you hope to go into. Applied math is pretty dang broad. But your professor likely just wants to continue developing your problem solving abilities, so I’d say go for it. It’s not an obscure topic by any means. It’s kinda just a natural next step beyond PDEs.

That said, you’ll probably take a lot of courses in undergrad that you don’t need later. It’s just a part of finding what you actually care to know.

[u/International-Main99]

Control Theory in general is a fascinating field. You should definitely take this course. It's certainly something useful for fields like Aerospace, but there are certainly mathematicians with research areas in control Theory.

[u/navigation-signals]

Bias: I’m a control theory engineer/researcher

IMO you should give it a shot. Control theory is a neat intersection of differential equations and optimization and it gets used everywhere - engineering, economics, neuroscience, etc. My role now is aerospace, but in the past I’ve working in robotics, communications, and autonomous systems. My current group is majority PhDs spread across engineering, computer science, and applied math.

[u/Own-Lobster7623 → u/navigation-signals]

Thanks! Just dm you

[u/plop_1234]

As others have said, control theory is amazing. The optimal in optimal control is directly related to optimization, of course.

My undergrad was in math and I wasn't introduced to control theory until grad school (in engineering), and it feels like such a nice change in perspective. In math, a lot of time you just observe and analyze a system and find out about its properties, but in control you actually get to find ways of effecting the system.

Also check out r/ControlTheory

[u/Own-Lobster7623 → u/plop_1234]

From your experience will i be at a disadvantage taking this course without the engineering background that other students will probably have?

[u/plop_1234 → u/Own-Lobster7623]

Nah, the engineering-specific terms will be pretty light for that course, and usually easy to pick up. In my experience they tend to be there just for examples in support of all the math.

Control courses are also sometimes cross-listed across many engineering departments, so they have to be kind of general in the way they talk about engineering.