Data classification and parameter estimation for the identification of piecewise affine models

This paper proposes a three-stage procedure for parametric identification of piece wise affine auto regressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the MIN PFS problem (partition into a minimum number of feasible subsystems) for a set of linear complementary inequalities derived from input-output data. Then, a refinement procedure reduces misclassifications and improves parameter estimates. The last stage determines a polyhedral partition of the regressor set via two-class or multi-class linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a fixed quantity. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. Ideas for efficiently addressing the MIN PFS problem, and for improving data classification are also discussed in the paper. The performance of the proposed identification procedure is demonstrated on experimental data from an electronic component placement process in a pick-and-place machine.