From 1fa4e2407138dcc3362b37ebee25f859c0a8c129 Mon Sep 17 00:00:00 2001 From: mforets Date: Tue, 2 Oct 2018 09:34:13 -0300 Subject: [PATCH] revise docstring --- src/Approximations/overapproximate.jl | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) diff --git a/src/Approximations/overapproximate.jl b/src/Approximations/overapproximate.jl index 8bbdfac5ea..1b7fe24860 100644 --- a/src/Approximations/overapproximate.jl +++ b/src/Approximations/overapproximate.jl @@ -179,7 +179,7 @@ polytope given a set of template directions. - `cap` -- intersection of a compact set and a polytope - `dir` -- template directions -- `kwargs` -- additional arguents that are passed to the support fumction algorithm +- `kwargs` -- additional arguents that are passed to the support function algorithm ### Output @@ -189,14 +189,15 @@ is given by an element of `dir`. ### Algorithm Let `di` be a direction drawn from the set of template directions `dir`. -Let `X` be the compact set and let `P` be the polytope; that we would like -to overapproximate the set `X ∩ H`. +Let `X` be the compact set and let `P` be the polytope. We overapproximate the +set `X ∩ H` with a polytope in constraint representation using a given set of +template directions `dir`. -Solving the univariate optimization problem `ρ(di, X ∩ Hi)` for each -half-space in the set `P` and then taking the minimum gives an overapproximation +The idea is to solve the univariate optimization problem `ρ(di, X ∩ Hi)` for each +half-space in the set `P` and then take the minimum. This gives an overapproximation of the exact support function. -This algorithm is inspired from [G. Frehse, R. Ray. Flowpipe-Guard Intersection +This algorithm is inspired from [G. Frehse, R. Ray. Flowpipe-Guard Intersection for Reachability Computations with Support Functions](https://www.sciencedirect.com/science/article/pii/S1474667015371809).