#2154 - Compute the overapproximation of the convex hull array of zonotopes with a zonotope recursively

src/Approximations/overapproximate.jl

@@ -1703,3 +1703,36 @@ function overapproximate(r::Rectification{N, <:AbstractZonotope{N}}, ::Type{<:Zo
 
     return Zonotope(c, remove_zero_columns(Gout))
 end
+
+"""
+    overapproximate(CHA::ConvexHullArray{N, <:AbstractZonotope{N}}, ::Type{<:Zonotope}) where {N}
+
+Overapproximation of the convex hull array of zonotopic sets.
+
+### Input
+
+- `CHA` -- convex hull array of zonotopic sets
+- `Zonotope` -- type for dispatch
+
+### Output
+
+A zonotope overapproximation of the convex hull array of zonotopic sets.
+
+### Algorithm
+
+This function iteratively applies the overapproximation algorithm for the
+convex hull of two zonotopes to the given array of zonotopes.
+"""
+function overapproximate(CHA::ConvexHullArray{N, <:AbstractZonotope{N}}, ::Type{<:Zonotope}) where {N}
+    arr = array(CHA)
+    n = length(arr)
+    if n == 1
+        return arr[1]
+    else
+        Zaux = overapproximate(ConvexHull(arr[1], arr[2]), Zonotope)
+        for k in 3:n
+            Zaux = overapproximate(ConvexHull(Zaux, arr[k]), Zonotope)
+        end
+        return Zaux
+    end
+end

test/unit_overapproximate.jl

@@ -373,4 +373,15 @@ for N in [Float64]
     y = set_variables("y", numvars=2, order=1)
     p = zero(y[1])
     @test get_linear_coeffs(p) == N[0, 0]
+
+    # Zonotope approximation of convex hull array of zonotopes
+    Z1 = Zonotope(N[3, 0], N[1 2 1; 1 1 2])
+    Z2 = Zonotope(N[1, 0], N[-2 1; 1 1])
+    Z3 = Zonotope(N[0, 0], N[1 0; 0 1])
+    @test overapproximate(ConvexHullArray([Z1]), Zonotope) == Z1
+    @test overapproximate(ConvexHullArray([Z1, Z2]), Zonotope) == overapproximate(ConvexHull(Z1, Z2), Zonotope)
+    Y = overapproximate(ConvexHullArray([Z1, Z2, Z3]), Zonotope)
+    @test Z1 ⊆ Y
+    @test Z2 ⊆ Y
+    @test Z3 ⊆ Y
 end