Manuscript VII-J@1 · VII-J.tex · corollary · d8c01b04

Corollary: Uncertainty margin

Directional paths and finite-time reachability › Support functions and robust margins · lines 821–848 · proof included or linked

VII-J@1#cor:velocitymargin

Suppose for all unit $n$ ,

h_{K_{sched}^{true}} (n) h_{K_{phys}^{true}} (n) \leq h_{K_{sched}} (n) + δ_{sched} (n), \geq h_{K_{phys}} (n) - δ_{phys} (n) .

h_{K_{phys}} (n) - h_{K_{sched}} (n) \geq δ_{phys} (n) + δ_{sched} (n),

then true velocity inclusion holds. Strict inequality gives a positive certified margin.

Proof. Combine the inequalities and apply Proposition prop:supportfunction.

Displayed formulas in this passage

unlabeled · line 824
$h_{K_{sched}^{true}} (n) h_{K_{phys}^{true}} (n) \leq h_{K_{sched}} (n) + δ_{sched} (n), \geq h_{K_{phys}} (n) - δ_{phys} (n) .$
unlabeled · line 835
$h_{K_{phys}} (n) - h_{K_{sched}} (n) \geq δ_{phys} (n) + δ_{sched} (n),$