The first stage of the Saturn V, for example, burned about 26 tons of material in total per second (https://en.wikipedia.org/wiki/Rocketdyne_F-1#Specifications). Therefore the rocket dynamics are changing... very quickly. How does the control/guidance system deal with this? Do they design 100 controllers that they gain-schedule? Thanks for your input!
According to "Description and Performance of the Saturn Launch Vehicle's Navigation, Guidance, and Control System", the control gain values make scheduled changes twice in each of the first two stages of ascent, and one more during the TLI burn, presumably reducing gain to avoid oversteering the lightened vehicle.
Note that Saturn V first-stage guidance was a pitch-vs-time program, concerned more with staying in a safe aerodynamic regime than with the exact trajectory.
I don't know how this compares with more modern systems; presumably the gain could be made a simple linear or polynomial function of time (since mass versus time should be fairly predictable).