Linear Combination

linear_combination(P1::SimpleSparsePolynomialZonotope,
                   P2::SimpleSparsePolynomialZonotope)

Compute the linear combination of two simple sparse polynomial zonotopes.

Input

• P1 – simple sparse polynomial zonotope
• P2 – simple sparse polynomial zonotope

Output

Linear combination of P1 and P2.

Notes

The linear combination of two sets $P₁$ and $P₂$ is defined as

\[\left\{\frac{1}{2}(1+λ)p₁ + \frac{1}{2}(1-λ)p₂ \mid p₁ ∈ P₁, p₂ ∈ P₂, λ ∈ [-1, 1]\right\}.\]

This method implements the algorithm described in Proposition 3.1.25 of [1].

[1] N. Kochdumper. Extensions of polynomial zonotopes and their application to verification of cyber-physical systems. 2021.