[tnecniv]

Depends on what you define to be advanced and deep.

If you know linear algebra, that opens up a variety of state space techniques. If you know a little optimization, that opens up optimal control, including the incredibly common LQR strategy. This stuff is typically accessible for an advanced undergrad with a few of the right prereqs.

But control theory is a deep field. You can find papers that use differential geometry, topology, information theory, etc. for designing control systems.