Nonlinear system identification by fuzzy piecewise affine models

In this paper, a new identification method of a piecewise affine model for a nonlinear system based on input-output data measurements is presented. In particular the identification of piecewise affine models of nonlinear single-input-single-output systems through Takagi-Sugeno models is considered. The basic idea in this paper is to decompose the nonlinear system into a set of piecewise affine systems. First, the least mean square method is used to identify the system in the neighborhood of each data point. Then the obtained parameter vectors are classified into groups. The center point of each group is considered as the parameter vector of the corresponding submodel. Groups are considered as fuzzy sets and their membership functions values at each data point is calculated using the distance between the parameter vector, which corresponds to the data point, and the center point. Using interpolation, the value of each membership function can be calculated at all points. Finally, the estimated output is obtained by Takagi-Sugeno fuzzy inference.