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Discrete transitions #169

Merged
merged 9 commits into from
May 13, 2020
Merged

Discrete transitions #169

merged 9 commits into from
May 13, 2020

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mforets
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@mforets mforets commented May 12, 2020

This is a start on handling discrete transitions for hybrid systems. Instead of storing the whole (R(X ∩ G ∩ I⁻) ⊕ W) ∩ I⁺ as a LazySet, we see this as a function X -> post_d(X). With this in mind we can easily dispatch on a given heuristics to compute this set (exactly if possible, or using template hulls, using a box approximation, combination of these, etc), without actually changing the hybrid loop code.

This PR has some cases to handle unions of polyhedra by using the distributive property for the intersection of unions.

Other important methods are missing, e.g. template hull overapproximation a la Frehse & Ray (https://www.sciencedirect.com/science/article/pii/S1474667015371809), so we can combine this with support function based reachability algorithms (LGG09).. but i would leave that for another PR.

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Apart from those comments it looks good.

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mforets commented May 13, 2020

The last commit contains some missing methods to handle UnionSetArray (we can remove them again once we admit this type as a <:LazySet). There are now two abstract interfaces, AbstractIntersectionMethod for methods to compute the intersection, and AbstractDisjointnessMethod for methods to compute disjointness. This incorporates some changes that we discussed above regarding what is a reasonable box aproximation: in fact, you can expect that SupportFunctionIntersection is a struct that has a template field, say ::BoxDirections, and we can just it it (as we can use any other template).

@mforets mforets merged commit 2a4c6dc into master May 13, 2020
@mforets mforets deleted the mforets/transitions branch June 17, 2020 11:07
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