Digital Library of Zielona Góra contains 63 052 digital objects
Object
Title: A computationally inexpensive algorithm for determining outer and inner enclosures of nonlinear mappings of ellipsoidal domains
Contributor:
Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Group publication title:
Abstract:
A wide variety of approaches for set-valued simulation, parameter identification, state estimation as well as reachability, observability and stability analysis for nonlinear discrete-time systems involve the propagation of ellipsoids via nonlinear functions. It is well known that the corresponding image sets usually possess a complex shape and may even be nonconvex despite the convexity of the input data. ; For that reason, domain splitting procedures are often employed which help to reduce the phenomenon of overestimation that can be traced back to the well-known dependency and wrapping effects of interval analysis. In this paper, we propose a simple, yet efficient scheme for simultaneously determining outer and inner ellipsoidal range enclosures of the solution for the evaluation of multi-dimensional functions if the input domains are themselves described by ellipsoids. ; The Hausdorff distance between the computed enclosure and the exact solution set reduces at least linearly when decreasing the size of the input domains. In addition to algebraic function evaluations, the proposed technique is - for the first time, to our knowledge - employed for quantifying worst-case errors when extended Kalman filter-like, linearization-based techniques are used for forecasting confidence ellipsoids in a stochastic setting.
Publisher:
Zielona Góra: Uniwersytet Zielonogórski
Resource Identifier:
DOI:
Pages:
Source:
AMCS, volume 31, number 3 (2021) ; click here to follow the link
Language:
License CC BY 4.0:
Rights:
Biblioteka Uniwersytetu Zielonogórskiego
Object collections:
- Digital Library of Zielona Góra > Repository > Faculties > Faculty of Computer, Electrical and Control Engineering
- Digital Library of Zielona Góra > Repository > Types of work > Articles
- Digital Library of Zielona Góra > Repository > Scientific journals and UZ publishing series > International Journal of Applied Mathematics and Computer Science (AMCS) > International Journal of Applied Mathematics and Computer Science (AMCS) (2021)
Last modified:
Jul 21, 2025
In our library since:
Jul 21, 2025
Number of object content hits:
13
All available object's versions:
https://zbc.uz.zgora.pl/publication/101377
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 31, number 1 (2021)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 31, number 2 (2021)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 31, number 3 (2021)
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International Journal of Applied Mathematics and Computer Science (AMCS), volume 31, number 4 (2021)
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