CAD.1:4.3 - Expose what the split removes

A useful way to derive a candidate is to introduce separate variables for decisions that were coupled in the whole problem. Initially constrain them to agree. For example, let a planner choose a nominal trajectory z while the plant state is x; keep the relation that says what plant behavior z represents. Only then relax that relation to obtain separately solvable subproblems.

For each relaxation, recover its price. Replacing equality by tracking allows an error; removing full dynamics requires a realizability condition; replacing continuous interaction by periodic exchange introduces stale information and intersample evolution. Removing future disturbance information requires a prediction or uncertainty treatment. These are concrete missing relations, not a generic “integration risk”.

Use MMP.9 when reduction is involved: derive the retained evolution and identify terms depending on omitted state, past inputs or unresolved quantities. A term does not disappear because the upper model has fewer states. Decide whether it is retained through memory, bounded as mismatch, supplied by a lower closed loop, or left as an unresolved limitation.

The first candidate is complete enough to continue when every removed interaction has a proposed receiving treatment in CAD.2 or CAD.3. A treatment may fail; naming it does not establish it.