Local Hammerstein modeling based on self-organizing map

This work presents a method to determine a local polynomial model from a finite number of measurements of the inputs and outputs for Hammerstein systems which are a zero-memory nonlinearity followed by a linear filter. Self-organizing map (SOM) is utilized to cluster the dynamics in the input-output joint space, where processing-elements (PEs) are extended with local models to enable the original algorithm to learn input-output relationships with reasonable accuracy. Moreover, in order to increase the approximation accuracy, local models are built by polynomial models instead of just linear models. The identification method is applied to two simulation examples of a discrete-time system and compared with other neural networks-based alternatives to demonstrate the performance and efficiency of the proposed technique.