On application of grid point sampling and SVD consolidation approach

An approach of grid point sampling and SVD consolidation has been proposed recently for nonlinear plant modeling and control system design. The approach calls for generating the plant´s linear approximations over a set of grid points in the domains of the state variables, and then conduct SVD consolidation to obtain a TS fuzzy model representation for the plant. Going a step further, grid point controllers may also be generated and then joined with the plant parameters for SVD reduction, thereby possibly resulting in new fuzzy structure over that of the original plant. Numerous works have been conducted for both cases. The present work aims to explore two outstanding issues regarding the approach. The first concerns its ability to extract inherent fuzzy structure of the plant, and the second studies the condition under which grid point controller design would maintain the fuzzy structure of the plant. We use a simple numerical example to illustrate the key ideas.