# Interval simulation of Narmax models based on computer arithmetic.

Guedes, Priscila F. S. and Peixoto, Márcia L. C. and Freitas, Otávio A R O and Barbosa, Alípio Monteiro and 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) Dynamical Systems; Error Propagation; Interval analysis; Intlab toolbox; Sistemas Dinˆamicos; Propaga¸c˜ao de erros; An´alise Intervalar; toolbox Intlab; Faculty of Science and Engineering > Electronic EngineeringFaculty of Science and Engineering > Research Institutes > Hamilton Institute 16864 https://doi.org/10.20906/CPS/CBA2018-0739 Erivelton Nepomuceno 17 Jan 2023 14:53 Yes 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