Determinação de aproximação linear por partes de funções não lineares para sistemas embarcados utilizando algoritmos genéticos

Abstract

In several applications in electronics, the generation of nonlinear function values using low-cost embedded systems is a problem. The nonlinear functions cannot be directly implemented due to restrictions of fixed-point calculations and limited resolution that are characteristics of the architecture of the processor employed. In this work, a procedure for determining piecewise linear approximation of nonlinear functions for a low-cost embedded system is presented. In order to solve this problem, a hierarchical evolutionary algorithm has been developed for determining the position and the minimal number of breakpoints and the minimal size of the look-up table for storing these breakpoints, for generating the approximated function values. The nonlinear function can be approximated using piecewise linear functions from the obtained breakpoints. The developed algorithm is tested using the case of approximating the first quadrant of a sine function, and the obtained results are presented for different resolutions for the input and output values generation.