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Matlab has been considered as a leader computational platform for many engineering fields. Well documented and reliable, Matlab presents as a great advantage its ability to increase the user productivity. However, Python and Octave are among some of the languages that have challenged Matlab. Octave and Python are well known examples of high-level scripting languages, with a great advantage of being open source software. The novelty of this paper is devoted to offer a comparison among these tree languages in the simulation of dynamical systems. We have applied the lower bound error to estimate the error of simulation. The comparison was performed with the chaotic systems Duffing-Ueda oscillator and the Chua's circuit, both identified with polynomial NARMAX. Octave presents the best reliable outcome. Nevertheless, Matlab needs the lowest time to undertake the same activity. Python has presented the worse result for the stop simulation criterion., Comment: SBAI 2019 - Simposio Brasileiro de Automacao Inteligente - Ouro Preto. 7 pages

This paper presents a study on the reduction of the sampling frequency of the current signals of an induction motor, the reductions are performed by means time-decimation technique for digital signal processing. We have used the Fast Fourier Transform to obtain the fault signal spectrum of broken bars. The results have shown how the decimation technique significantly reduces the number of operations and the time required to calculate the Fast Fourier Transform without loss of information. This approach provides a better performance of embedded systems for fault diagnosis based on characteristic of amplitude signal modulation., Comment: in Portuguese

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., Comment: CBA 2018 - XXII Congresso Brasileiro de Automatica, Joao Pessoa, p. 1-6

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, Comment: DINCON 2017 - Conferencia Brasileira de Dinamica, Controle e Aplicacoes. Sao Jose do Rio Preto. Brazil. 7 pages

The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed and developed for its calculation. The present work proposes a method for the calculation of the largest Lyapunov exponent, based on conditional number of the function, which describes the loss of bits in the simulation based on relative rounding error. Four discrete maps are used to show the effectiveness of the proposed method., Comment: DINCON 2017 - Conferencia Brasileira de Dinamica, Controle e Aplicacoes - Sao Jose do Rio Preto - Brazil. 7 pages