CAD.2:4.1 - Define the exchanged behavior

Use MMP.18 to establish meanings, units, coordinate frames, observation times, validity intervals and the operation performed between messages. A target, an input, an output trajectory and a constraint are different commands. State which one the lower computation receives.

Choose how the upper model represents the lower behavior. For a planning state z and plant state x, a reconstruction Pz can define an error e=x-Pz. A measured projection z=\Pi x is a different map. Even if \Pi P=I, initializing z=\Pi x leaves e=(I-P\Pi)x, which need not vanish.

If the controlled quantity is y=Cx and the planner predicts y_p=C_pz, then

y-y_p=Ce+(CP-C_p)z.

Output agreement requires the second term to vanish or be included in the bound. State reconstruction, output matching and physical identity are separate questions.