Reducing the wrapping effect of set computation via Delaunay triangulation for guaranteed state estimation of nonlinear discrete-time systems

Abstract

Set computation methods have been widely used to compute reachable sets, design invariant sets and estimate system state for dynamic systems. The wrapping effect of such set computation methods plays an essential role in the accuracy of their solutions. This paper studies the wrapping effect of existing interval, zonotopic and polytopic set computation methods and proposes novel approaches to reduce the wrapping effect for these set computation methods based on the task of computing the dynamic evolution of a nonlinear uncertain discrete-time system with a set as the initial state. The proposed novel approaches include the partition of a polytopic set via Delaunay triangulation and also the representation of a polytopic set by the union of small zonotopes for the following set propagation. The proposed novel approaches with the reduced wrapping effect has been further applied to state estimation of a nonlinear uncertain discrete-time system with improved accuracy. Similar to bisection for interval and zonotopic sets, Delaunay triangulation has been introduced as a set partition tool for polytopic sets, which has opened new research directions in terms of novel set partition, set representation and set propagation for reducing the wrapping effect of set computation.

Publication DOI: https://doi.org/10.1007/s00607-024-01275-0
Divisions: College of Engineering & Physical Sciences > School of Engineering and Technology > Mechanical, Biomedical & Design
College of Engineering & Physical Sciences > Smart and Sustainable Manufacturing
College of Engineering & Physical Sciences
Aston University (General)
Funding Information: This work was supported in part by the start-up grant of Aston University. The authors are very grateful for anonymous reviewers’ comments and suggestions to improve the paper significantly.
Additional Information: Copyright © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
Uncontrolled Keywords: Set computation,Wrapping effect,Nonlinear systems,State estimation
Publication ISSN: 1436-5057
Last Modified: 02 Dec 2024 09:04
Date Deposited: 15 Mar 2024 17:21
Full Text Link:
Related URLs: https://link.sp ... 607-024-01275-0 (Publisher URL)
http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2024-05
Published Online Date: 2024-03-05
Accepted Date: 2024-02-19
Authors: Wan, Jian (ORCID Profile 0000-0001-5904-9261)
Jaulin, Luc

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