arXiv subjects

Joseph K. Scott

Publications and source records attributed to Joseph K. Scott.

4 recordsLinked to original sources

arXiv2026

Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes and polyhedral relaxations

This paper presents a new algorithm for set-based state estimation of nonlinear discrete-time systems. A key step in such algorithms is to propagate a set (often a zonotope or constrained zonotope) through a nonlinear function. Existing methods accomplish this through conservative linearization procedures that are known to lead to severe overestimation in many cases. Here, we propose an alternative that avoids linearization using the so-called factorable representation of nonlinear functions. We use a recursive polyhedral relaxation technique based on this representation that is well-established in the global optimization literature but has not previously been used for set-based estimation. This technique is combined with constrained zonotope (CZ) technology to avoid the limitations of recursive computations with polyhedra in halfspace representation. The resulting state estimation method is fully automated, has attractive computational complexity (with one caveat discussed herein), and can provide significantly tighter enclosures than those resulting from linearization procedures in many cases. Numerical examples highlight the advantages of this approach relative to existing CZ methods based on the Mean Value Theorem and Difference of Convex functions (DC) programming.

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arXiv2025

Reachability Analysis of Nonlinear Discrete-Time Systems Using Polyhedral Relaxations and Constrained Zonotopes

This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to propagate CZs through nonlinear functions, which is normally done using conservative linearization techniques. The new propagation method provides better approximations than those resulting from linearization procedures, leading to significant improvements in the computation of reachable sets in comparison to other CZ methods from the literature. Numerical examples highlight the advantages of the proposed algorithm.

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arXiv2025

ZETA: a library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems

This paper introduces ZETA, a new MATLAB library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems. It features user-friendly implementations of set representations based on zonotopes, namely zonotopes, constrained zonotopes, and line zonotopes, in addition to a basic implementation of interval arithmetic. This library has capabilities starting from the basic set operations with these sets, including propagations through nonlinear functions using various approximation methods. The features of ZETA allow for reachability analysis and state estimation of discrete-time linear, nonlinear, and descriptor systems, in addition to active fault diagnosis of linear systems. Efficient order reduction methods are also implemented for the respective set representations. Some examples are presented in order to illustrate the functionalities of the new library.

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arXiv2019

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

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.

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