Zonotopic overapproximation of a taylor model with template zonotope

[mforets]

Let F = (p(x₀, t), I) be an n-dimensional TM flowpipe, x₀ ∈ X₀, t ∈ [0, δ]. Two ideas are outlined in [1] (we may split these into smaller issues):

• using a conservative linearization of the TM.
• using a templated zonotope.

Question: how do we check for containment?

Refs:

• [1] Section 4.3, Chen, X. (2015). Reachability analysis of non-linear hybrid systems using taylor models (Doctoral dissertation, Fachgruppe Informatik, RWTH Aachen University).

• linear_polynomial in https://github.com/JuliaDiff/TaylorSeries.jl/pull/206/files

[mforets]

using a conservative linearization of the TM.

This method was added in Lazysets v1.13.0.

using a templated zonotope.

This is not implemented yet (described in Chen's thesis).