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Generalize discretization for GLGM06 #713

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Jan 16, 2020
Merged

Generalize discretization for GLGM06 #713

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b5ecc85
generalize zonotope conversion for GLGM06
mforets Nov 18, 2019
36dcb83
add test
mforets Nov 18, 2019
bfcf866
Update src/ReachSets/discretize.jl
mforets Nov 20, 2019
cfd68b2
Update src/ReachSets/discretize.jl
mforets Nov 20, 2019
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27 changes: 19 additions & 8 deletions src/ReachSets/discretize.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -701,8 +701,8 @@ end

# version using concrete operations with zonotopes
function _discretize_interpolation_homog(X0, ϕ, Einit, set_operations::Val{:zonotope})
Einit = convert(Zonotope, Einit)
Z1 = convert(Zonotope, X0)
Einit = _convert_or_overapproximate(Zonotope, Einit)
Z1 = _convert_or_overapproximate(Zonotope, X0)
Z2 = linear_map(ϕ, minkowski_sum(Z1, Einit))
Ω0 = overapproximate(ConvexHull(Z1, Z2), Zonotope)
return Ω0
Expand All @@ -711,11 +711,11 @@ end
# version using concrete operations with zonotopes
function _discretize_interpolation_inhomog(δ, U0, U, X0, ϕ, Einit, Eψ0, A, sih, Phi2Aabs, set_operations::Val{:zonotope})
n = size(A, 1)
Einit = convert(Zonotope, Einit)
Eψ0 = convert(Zonotope, Eψ0)
Z1 = convert(Zonotope, X0)
Einit = _convert_or_overapproximate(Zonotope, Einit)
Eψ0 = _convert_or_overapproximate(Zonotope, Eψ0)
Z1 = _convert_or_overapproximate(Zonotope, X0)
ϕX0 = linear_map(ϕ, Z1)
U0 = convert(Zonotope, U0)
U0 = _convert_or_overapproximate(Zonotope, U0)
δI = Matrix(δ*I, n, n)
δU0 = linear_map(δI, U0)
Z2 = reduce(minkowski_sum, [ϕX0, δU0, Eψ0, Einit])
Expand All @@ -727,8 +727,8 @@ function _discretize_interpolation_inhomog(δ, U0, U, X0, ϕ, Einit, Eψ0, A, si
elseif U isa VaryingInput
Ud = Vector{LazySet}(undef, length(U))
for (k, Uk) in enumerate(U)
Eψk = convert(Zonotope, sih(Phi2Aabs * sih(A * Uk)))
Uk = convert(Zonotope, Uk)
Eψk = _convert_or_overapproximate(Zonotope, sih(Phi2Aabs * sih(A * Uk)))
Uk = _convert_or_overapproximate(Zonotope, Uk)
δUk = linear_map(δI, Uk)
Ud[k] = minkowski_sum(δUk, Eψk)
end
Expand Down Expand Up @@ -887,3 +887,14 @@ function _discretize_interval_matrix_inhomog(U, Ω0_homog, linear_maps,
end
return Ω0, Ud
end

# fallback implementation for conversion (if applicable) or overapproximation
function _convert_or_overapproximate(X::Type{<:AbstractPolytope}, Y::LazySet)
if applicable(convert, X, Y)
return convert(X, Y)
elseif applicable(overapproximate, Y, X)
return overapproximate(Y, X)
else
return convert(X, overapproximate(Y, Hyperrectangle))
end
end
4 changes: 4 additions & 0 deletions test/Reachability/solve_continuous.jl
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Expand Up @@ -173,6 +173,10 @@ s = solve(IVP(LCS(A), X0), Options(:T=>0.1), op=GLGM06(:max_order=>15))
# affine system, x' = Ax + Bu
s = solve(IVP(CLCCS(A, B, nothing, U), X0), Options(:T=>0.1), op=GLGM06())

# initial set which cannot be converted to a zonotope
X0 = Ball2(ones(4), 0.1)
s = solve(IVP(LCS(A), X0), Options(:T=>0.1), op=GLGM06())

# ======================
# Unbounded-time setting
# ======================
Expand Down