The Lower Bound Error for polynomial NARMAX using an Arbitrary Number of Natural Interval Extensions
Priscila Fernanda da Silva Guedes1; Márcia Luciana da Costa Peixoto1; Alípio Monteiro Barbosa2; Samir Angelo Milani Martins1; Erivelton Geraldo Nepomuceno1
1 Universidade Federal de São João del-Rei; 2 Centro Universitário Newton Paiva
Resumo
The polynomial NARMAX (Nonlinear AutoRegressive Moving Average model with eXogenous input) is a model that represents the dynamics of physical systems. This polynomial contains information from the past of the inputs and outputs of the process, that is, it is a recursive model. In digital computers this generates the propagation of the rounding error. Our procedure is based on the estimation of the maximum value of the lower bound error considering an arbitrary number of pseudo-orbits produced from different natural interval extensions, and a posterior Lyapunov exponent calculation. We applied successfully our technique for two identified models of the systems: sine map and Duffing-Ueda oscillator.