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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!

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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:

http://www.lpi.usra.edu/meetings/marsconcepts2012/pdf/4193.pdf

And you can find more here : https://scholar.google.com/citations?hl=en&user=xZvK9z0AAAAJ&view_op=list_works&sortby=pubdate

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