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

TL;DR

This paper introduces new constrained zonotope-based methods for set-valued state estimation in nonlinear discrete-time systems, improving enclosure tightness while maintaining computational efficiency.

Contribution

It proposes mean value and first-order Taylor extensions for propagating constrained zonotopes, enhancing accuracy over existing zonotope methods.

Findings

Tighter prediction enclosures than traditional zonotopic methods.

Enhanced update enclosures due to better intersection representation.

Maintains computational efficiency comparable to zonotope-based approaches.

Abstract

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.