# Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems

arXiv: https://arxiv.org/abs/1908.09950 · HTML: https://mlsanity.com/paper/1908.09950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2019.

## Built on by (most cited first, 1 of 1)

- [Data-driven Set-based Estimation of Polynomial Systems with Application to SIR Epidemics](https://mlsanity.com/paper/2111.04704/) (2021)

## Abstract (arXiv)

This paper presents new methods for set-valued state estimation of nonlinear discrete-time systems with unknown-but-bounded uncertainties. A single time step involves propagating an enclosure of the system states through the nonlinear dynamics (prediction), and then enclosing the intersection of this set with a bounded-error measurement (update). When these enclosures are represented by simple sets such as intervals, ellipsoids, parallelotopes, and zonotopes, certain set operations can be very conservative. Yet, using general convex polytopes is much more computationally demanding. To address this, this paper presents two new methods, a mean value extension and a first-order Taylor extension, for efficiently propagating constrained zonotopes through nonlinear mappings. These extend existing methods for zonotopes in a consistent way. Examples show that these extensions yield tighter prediction enclosures than zonotopic estimation methods, while largely retaining the computational benefits of zonotopes. Moreover, they enable tighter update enclosures because constrained zonotopes can represent intersections much more accurately than zonotopes.