Historically, endoatmospheric guidance for launch ascent has been open loop and suboptimal. Recently, however, it seems as though there has been renewed interest in determining optimal endoatmospheric ascent. For example, Ping Lu's paper: Closed-Loop Endoatmospheric Guidance.

My question has two parts:

  1. Are closed-loop guidance laws typically used for modern launch vehicles, or do most still use open-loop guidance for the endoatmospheric phase?
  2. How is SpaceX applying constraints on their first-stage guidance such that the first stage booster has the propellant and "initial" state to return to launch site or land on a droneship? Where, "initial" refers to the moment of second stage separation. SpaceX uses G-FOLD, Guidance for Fuel Optimal Large Divert, to determine the optimal guidance for landing the first stage booster. Research was previously done on splash-down constraints on the first-stage of the Ariane V, such that the first-stage would splash down in the first orbit. This however, seems to be insufficient for the requirements of an RTLS mission.
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    $\begingroup$ I've made an adjustment to your title so that it better matches the question you are asking. Feel fee to edit further! $\endgroup$ – uhoh Dec 20 '18 at 7:05

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