There’s one really important aspect of starship control that this article mentions... starship control is stochastic. Spacex needs to minimize the area of an ellipse that represents the likely touchdown area of the craft. To do this they use another trick... they continuously recompute the optimal trajectory, in real time. Lars Blackmore has a paper on the process!
Not to accuse spaceX of anything, but I've witnessed companies sell 'hyper-localised weather" where they take public weather information and average the nearest two datapoints to you.
So I always take 'secret' 'proprietary' data and algorythms with a bit of salt, as almost every time I dug into them, it was all spin on previous public stuff.
In this case, SpaceX is actually landing those Falcon boosters pretty reliably now. So maybe their secret proprietary stuff isn't as advanced as they make it out to be, but whatever they're doing it does seem effective.
You can implement it as MPC and minimize e.g. the trace of the covariance matrix that describes the state uncertainty. Wrote my thesis on something similar.
