CAD.4:4.3 - Include execution in the design equations

Use MMP.22 to turn the mathematical operation into a workable computation. Identify the data needed when the operation starts, the work that can be prepared ahead, the result required at its deadline, and what must happen if it is unavailable.

A necessary timing comparison is

C_{\mathrm{fast}}\leq T_{\mathrm{fast}},\qquad C_{\mathrm{plan}}\leq T_{\mathrm{plan}},

where C bounds execution under the selected implementation. These isolated inequalities are not sufficient on a shared processor: blocking, interference, communication and scheduling must fit the deadlines together. An operation count or mean runtime is not a worst-case execution bound.

If planning finishes one period after its observation, model that delay and the command that controls the intervening period. Preparing a future segment can make the delay harmless for a predetermined reference but not automatically for a newly observed obstacle. Increasing the processor speed changes the feasible architecture set; increasing the assumed speed in a spreadsheet does not.

Use the implementation to test unit conversions, numerical tolerances, update order, saturation and reset behavior. A numerical optimizer’s constraint tolerance belongs in the margin analysis if it can consume physical clearance. Verify that the lower law actually executed is the law used in CAD.2.

If an online solver returns only a partial iterate, separate the time spent solving from the test that permits applying its output. A qualified acceptance rule may allow a feasible inexact result and otherwise keep an admissible prior command or plan. Include the cost of that test and the conditions for progress; a timeout says nothing about admissibility, and feasibility alone does not establish progress. The command-governor alternative in :11 is one developed construction, not a fallback rule for every optimizer.