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Discretize using concrete operations with zonotopes #512

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mforets opened this issue Mar 5, 2019 · 2 comments
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Discretize using concrete operations with zonotopes #512

mforets opened this issue Mar 5, 2019 · 2 comments
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@mforets
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mforets commented Mar 5, 2019

For the zonotopes set representation, Minkowski sum and linear map can be computed efficiently. The proposal is to offer a way to compute

Ω0 = ConvexHull(X0, ϕ*X0  δ*U  □α)

in discretize returning the convex hull of two zonotopes. Then, we can use the existing function in LazySets.Approximations.overapproximate to convert it back to a zonotope.

@mforets mforets added the feature label Mar 5, 2019
@mforets
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mforets commented Mar 8, 2019

This option applies to different approximation models, so i think that it is better to add it as a separate option. What woud be a good name? The option refers to the set type, or representation, used for the initial states and for the transformed inputs. Now we are using "lazy" set types: the initial states of the discretized system are a lazy convex hull.

@schillic
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schillic commented Mar 8, 2019

We can add a new algorithm, for instance of the name "zonotopes".

mforets added a commit that referenced this issue Mar 8, 2019
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