Circuit implementation of piecewise-affine functions based on lattice representation

Abstract

This paper introduces a digital architecture to implement piecewise-affine (PWA) functions based on representation methods from the lattice theory. Given an explicit and continuous PWA function, the parameters required to implement the lattice approach can be obtained by an off-line preprocessing that can be automated. Other advantages of the proposal are that it implements a continuous PWA function with potentially no errors and the minimum number of parameters to store. This has been proven experimentally by implementing the proposal in a Xilinx FPGA and comparing its performance with other implementations, all of them addressing a typical non linear control problem.