INTERVAL SIMULATION OF NARMAX MODELS BASED ON COMPUTER ARITHMETIC

PRISCILA  F. S. GUEDES; MÁRCIA  LUCIANA DA COSTA PEIXOTO; OTÁVIO  AUGUSTO RODRIGUES DE OLIVEIRA FREITAS; ALÍPIO  MONTEIRO BARBOSA; SAMIR  ANGELO MILANI MARTINS; ERIVELTON GERALDO NEPOMUCENO

doi:10.20906/CBA2022/411

PRISCILA F. S. GUEDES UFSJ - Universidade Federal de São José do Del Rei
MÁRCIA LUCIANA DA COSTA PEIXOTO UFSJ - Universidade Federal de São José do Del Rei
OTÁVIO AUGUSTO RODRIGUES DE OLIVEIRA FREITAS UFSJ - Universidade Federal de São José do Del Rei
ALÍPIO MONTEIRO BARBOSA Centro Universitário Newton Paiva
SAMIR ANGELO MILANI MARTINS UFSJ - Universidade Federal de São José do Del Rei
ERIVELTON GERALDO NEPOMUCENO UFSJ - Universidade Federal de São José do Del Rei

DOI: https://doi.org/10.20906/CBA2022/411

Keywords: Dynamical systems, Error propagation, Interval analysis, Intlab toolbox

Abstract

System identication 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 nite 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.