There is a lot of literature if you search the terms dynamic matrix control, optimal control theory, model predictive control, reinforcement learning.

The main idea is that control problems can be posed as optimization problems where we try to achieve some goal (financial / stability etc) while satisfying some hard restrictions.

For example try to change lines gracefully and fast on the highway without crashing on another car.

For your particular case, if you want something dirt cheap (computationally) and reliable then the PID is a great first step.

My understanding is that PID does not work as well for Mulitple Input Multiple Output systems compared with "modern control theory." See the "Analysis techniques - frequency domain and time domain" and "Classical SISO System Design" sections of below Wikipedia article.

https://en.m.wikipedia.org/wiki/Control_theory