A PWA model identification method for nonlinear systems using hierarchical clustering based on the gap metric

Abstract

A piecewise affine (PWA) model identification method for nonlinear systems using hierarchical clustering based on the gap metric is proposed. The model parameter estimation is realized by clustering input-output data according to the local models. We initially introduce the gap metric to analyze the similarity between the local models from the perspective of the system, which distinguishes the proposed method from other identification methods that only focus on data features. To determine the optimal number of submodels, the hierarchical clustering aimed at the identification error minimization is addressed. Furthermore, Softmax regression is adopted to completely partition the valid region of a PWA model. Particle swarm optimization (PSO) algorithm is applied to simultaneously update the partition boundaries and model parameters in order to avoid the mismatch between them. Case studies on the multivariable pH neutralization process demonstrate that the proposed method achieves more accurate and stable identification.