Inclusion conditions for the Constrained Polynomial Zonotopic case
This work addresses a challenge in set operations for non-convex geometries, offering a method for inclusion testing in CPZs, which is incremental as it builds on existing CPZ representations.
The paper tackles the problem of testing inclusion between constrained polynomial zonotopes (CPZs), which are non-convex sets, by proposing novel nonlinear encodings that provide sufficient conditions and integrate them into optimization frameworks.
Set operations are well understood for convex sets but become considerably more challenging in the non-convex case due to the loss of structural properties in their representation. Constrained polynomial zonotopes (CPZs) offer an effective compromise, as they can capture complex, typically non-convex geometries while maintaining an algebraic structure suitable for further manipulation. Building on this, we propose novel nonlinear encodings that provide sufficient conditions for testing inclusion between two CPZs and adapt them for seamless integration within optimization frameworks.