Zonotopic Filtering for Uncertain Nonlinear Systems: Fundamentals, Implementation Aspects, and Extensions [Applications of Control]

When the bounds of uncertain variables are known, they can be represented by sets, such as polyhedra, polytopes, zonotopes, constrained zonotopes (CZs), parallelotopes, intervals, strips, and ellipsoids [1]-[4]. These sets are illustrated in Figure 1 for the 2D case. While interval arithmetic defines interval sets [1], [2], affine arithmetic (which is an extension of interval arithmetic) allows for defining more general sets, such as zonotopes [3]. This article focuses on set-based state estimation using interval and zonotopic sets (see "Summary").