I was surprised as well when I first learned about them...Control Theory as a formalized scientific/engineering discipline didn't even exist until after the proliferation of the Centrifugal Governor, which has some varied accounting of its history, but generally is not quoted any earlier than the late 1700s.

One of the beauties of the algorithm is how well it scales to complexity. It can be implemented in something as simple as a mechanical or hydrolic controller or DSP, but can also be used in heavily modified forms that take advantage of advances in Machine Learning, OR/Optimization, etc.

The Greeks and Romans to my limited knowledge weren't very good at continuous maths. That whole domain of math seems fairly recent, at least in the western world. Calculus itself wasn't invented until Isaac Newton or a little before.