CAD.Reference:4.3 - Connect dynamics, decisions and computation by their actual quantities

The common quantities make the reasoning inspectable. The task sets a demanded progression, cost or reachability condition. A candidate command class S says what the planner may send. The interface yields an error evolution, such as e^+=Fe+Hz+Gv+w. S and the mismatch domain bound its forcing. An invariant E bounds the difference between nominal and realized behavior. The inclusions Pz+E\subseteq X and Qz+Rv+KE\subseteq U then restrict S. These are the exact-state formulas. When feedback uses an estimate, CAD.5:4.7 adds estimation error to both the forcing and the input allowance.

These are mutually constraining statements, not independent labels. Enlarging S can enlarge E, which can make the proposed S inadmissible. Reducing E by changing a gain can increase the size of KE and consume more actuator authority. Reducing the planning model can shorten computation while increasing H or the mismatch set. A longer update interval can fit the computation and enlarge the change the tracker must absorb. A bigger model can remove an important residual but leave no time to use the result.

Thus “more accurate”, “faster” and “more robust” are incomplete comparisons until their quantities and costs are named. A more accurate nominal prediction does not imply a smaller implemented error if it arrives late. A smaller tracking error does not imply a better task result if the permitted command range becomes too small. A feasible computation does not imply safe execution if its output is applied at the wrong instant.

The mathematical construction does not eliminate the engineering choice. It makes the choice explicit: accept a smaller envelope, change an interface, spend more computation, use another sensor or actuator, or revise an impossible requirement. SYSE.6 remains the place for that larger system decision.