A study of numerical nonlinear control using piecewise linear system approximation

For differential geometry based control, the approximation and control scheme studied attempts to resolve the difficulties of accurate modeling and inconvenient calculations by casting the original problem into a simpler form. Given data from the nonlinear system, its state-space is partitioned into cells and an affine-in-state model is determined for each cell by least squares identification. The cell models then constitute an overall piecewise linear system model. Feedback linearization techniques are then performed on the piecewise linear model. The calculations needed to perform the feedback linearization within each cell are shown to be in a simple generic form. The overall controller is formed by joining the individual cell controllers. The results of implementing this control scheme on an example second order nonlinear system show that the resulting controller's performance approaches that of the standard input-state linearization controller.