It's interesting to think about how the optimal strategy to land the lander would look like. If the distance to the moon was large, I would expect 4 phases: 1: Turn the lander towards the moon 2: Constant thrust towards the moon 3: Turn the lander away from the moon 4: Constant thrust away from the moon But if the initial distance is small enough, turning it around might not be worth it or even possible. So the optim…
time optimal landing lends techniques from bang-bang control (e.g. starting with v=0, max thrust towards the target, before flipping around half way and max thrust away from target)
fuel optimal landing (incuding RCS) technique would depend on the available time to turn retrograde (pointy end pointing away from direction of movement). if the duration before the decelerating burn is T1 (so t1 = t0+T1), the smallest possible rcs impulse would be applied so that at t1-T_st the lander is pointing retrograde (retrograde at t1), with T_st being the time needed to cancel the initial rcs impulse. For the deceleration of the lander, fuel optimal landing includes a single burn, constantly retrograde, so that at t_end the lander altitude is 0, and both the vertical and horizontal velocity components are 0.
The time t1 to start that burn depends on the maximum thrust available, the rate of mass change when firing the rocket (not modelled in the game), the initial velocity etc.
in this simple case, model predictive control is not needed, and an LQR (linear quadratic regulator) is sufficient to achieve optimality
source: rocket scientist with control theory background. I remember this example (a bit more realistically modelled) being a project during my studies