Earlier quoted context omitted.
MIMO and nonlinear control theories are probably some of the hardest topics in all of engineering. SpaceX control system also has to compensate for the fuel moving inside their rockets so the control algorithms probably involve some kind of fast numerical fluid simulation. Another interesting thing SpaceX is doing is to use consumer-grade chips in triple redundancy configurations instead of using $100,000+ radiation-…
I always thought the liquid sloshing would be one of the hardest to simulate (considering how chaotic fluid mechanics is). Interestingly, I think this caused the 2nd Falcon launch to fail (the LOX sloshing).
I think it's a huge problem when re-lighting the engines in orbit, though.