INTERVAL SIMULATION OF NARMAX MODELS BASED ON COMPUTER ARITHMETIC
Priscila Fernanda da Silva Guedes1; Márcia Luciana da Costa Peixoto1; Otávio Augusto Rodrigues de Oliveira Freitas1; Alípio Monteiro Barbosa2; Samir Angelo Milani Martins1; Erivelton Geraldo Nepomuceno1
1 Universidade Federal de São João del-Rei; 2 Centro Universitário Newton Paiva
Baixar PDF doi:10.20906/CPS/CBA2018-0739
Resumo
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.
Palavras-chave: Dynamical Systems; Error Propagation; Interval analysis; Intlab toolbox