A Genetic Algorithm Based Clustering Approach for Piecewise Linearization of Nonlinear Functions

In recent years, piecewise linearization has developed as an attractive tool for the representation of various complex nonlinear systems. The piecewise linearization of individual functions provide a platform for the piecewise affine approximation of nonlinear systems containing a large number of scaler valued nonlinear functions. Inspite of the wide application of piecewise linearization, the optimal approximation of a continuous time nonlinear function by the minimum number of piecewise linearised functions has not been addressed properly in literature. This paper deals with an evolutionary optimization based clustering approach for obtaining the optimal piecewise linear approximation of a class of nonlinear functions. The technique is based on the trade-off between increasing the approximation accuracy and simplifying the approximation by the minimum number of linearized sectors. The technique has been successfully applied to some common nonlinear functions.