Guedes, Priscila F. S., Peixoto, Márcia L. C., Freitas, Otávio A R O, Barbosa, Alípio Monteiro, Martins, Samir Angelo Milani and Nepomuceno, Erivelton (2018) Interval simulation of Narmax models based on computer arithmetic. In: XXII Congresso Brasileiro de Automática, January 2018.
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Abstract
System identification is an important area of science, which aims to describe the characteristics
of the system, representing them by mathematical models. Since many of these models can be seen as recursive
functions, it is extremely important to control the errors in these functions, because small errors introduced in
each computational step can grow exponentially due to the sensitivity to initial conditions present in this type
of functions. One of the ways to control rounding and truncation errors is through interval arithmetic, since
it is not possible to represent all numbers in the computer because of the finite representation in them. Thus,
in arithmetic interval a number is represented by an interval in which the true number is within that interval.
In this manuscript we developed an algorithm that performs the operations of interval arithmetic using basic
functions. We have compared compared our results with the Matlab-toolbox Intlab. Numerical experiments have
shown that our method is superior producing narrower intervals.
Resumo— Identifica¸c˜ao de sistemas ´e uma ´area importante da ciˆencia, tendo como objetivo descrever as
caracter´ısticas do sistema, representando-as por equa¸c˜oes matem´aticas. Como muitas dessas equa¸c˜oes podem
ser vistas como fun¸c˜oes recursivas, ´e de extrema importˆancia controlar os erros nessas fun¸c˜oes, j´a que pequenos
erros introduzidos a cada passo computacional pode crescer exponencialmente devido a sensibilidade a condi¸c˜oes
iniciais presente nessas fun¸c˜oes. Uma das formas de controlar erros de arredondamento e truncamento ´e atrav´es
da aritm´etica intervalar, uma vez que n˜ao ´e poss´ıvel representar todos os n´umeros no computador devido `a
representa¸c˜ao finita dos mesmos. Ent˜ao, na aritm´etica intervalar, um n´umero ´e representado por um intervalo
em que o verdadeiro n´umero se encontra nesse intervalo. Foi desenvolvido um algoritmo que realiza as opera¸c˜oes
da aritm´etica intervalar a partir de fun¸c˜oes b´asicas do Matlab. Os resultados foram comparados com o toolbox
do Matlab, Intlab. Experimentos num´ericos mostraram que os intervalos obtidos pelo nosso m´etodos s˜ao menores
do que aqueles obtidos no Intlab.
Item Type: | Conference or Workshop Item (Paper) |
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Keywords: | Dynamical Systems; Error Propagation; Interval analysis; Intlab toolbox; Sistemas Dinˆamicos; Propaga¸c˜ao de erros; An´alise Intervalar; toolbox Intlab; |
Academic Unit: | Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute |
Item ID: | 16864 |
Identification Number: | 10.20906/CPS/CBA2018-0739 |
Depositing User: | Erivelton Nepomuceno |
Date Deposited: | 17 Jan 2023 14:53 |
Refereed: | Yes |
URI: | https://mu.eprints-hosting.org/id/eprint/16864 |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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