Which are the main control theories behind the landing maneuvers of the Falcon 9? For the hovering part, as it approaches the landing surface, I guess the inverted pendulum control approaches would do it. But what about the control from stage separation till it the reentry burn? Any textbook references appreciated!
One of the key control algorithms involved is called G-FOLD, or Guidance for Fuel-Optimal Large Diverts. This is something that JPL has been working on for Mars landings, and some people involved have actually went to work for SpaceX a few years ago. Here is a high level description:
And you can find more here : https://scholar.google.com/citations?hl=en&user=xZvK9z0AAAAJ&view_op=list_works&sortby=pubdate