This answer to the question How was the Space Shuttle Orbiter used for ISS Reboost? describes a procedure I never knew happened. When the shuttle was docked to the ISS it sometimes used its rear reaction control thrusters to boost the ISS' orbital altitude, something that has to be done regularly to compensate for drag.
A small part of that answer says:
Two down-firing jets were used simultaneously on this flight.
Other VRCS jets fired as needed to control undesired rotations of the stack and maintain the commanded attitude.
After the reboost was complete, control of the stack was handed back to the ISS control system.
During this time it seems the ISS shuts down its own attitude control and the shuttle takes over. I think this means that the Shuttle's ADCS has to imagine that it is no longer just the Shuttle, but the whole Shuttle + ISS superstructure, and behave accordingly.
If the whole thing could be treated as a single rigid body, then this might be as simple as updating the moment of inertia tensor. But this combination may not be rigid enough for that. If you apply a torque at one end of the ISS, it could bend or even oscillate, and depending on the time constants set in the ADCS control system, those oscillations might even become unstable.
What were the considerations necessary to implement ADCS for the Shuttle + ISS superstructure in the Shuttle's computer? Did it have to be calibrated experimentally by "pinging" one of the thrusters that were off-axis and measuring the flexure of the system, oscillation time constant and decay rate?
Or did they just model it on the ground, dock, and start boosting away?