Geometric Clustering and Parameter Estimation in Multiple Local Linear Model Identification

Abstract

A novel geometric method for local linear model (LLM) identification of nonlinear systems involving clustering and principal component analysis (PCA) is developed. This is done in three main steps: The estimation data product set is first clustered in a sufficiently large number of crisp clusters spanning low-rank subspaces; then its elements are reclassified by merging the closest clusters spanning similar subspaces by using PCA based subspace clustering; finally the partitioning parameters of the system working space and the parameters of the LLMs are retrieved simultaneously from the statistical and geometric properties of the yielding affine subspace segmentation, respectively. The benefits of this algorithm are manifold: its black box and ‘normal’ data driven estimation feathers, its LLM structure reduction capability, its robustness with respect to noise, and its computation efficiency due to its simplicity and batch feature. Its effectiveness has been tested by simulation, and results are quite satisfactory.