An iterative optimization-based approach to piecewise affine system identification

In this paper, we propose an iterative approach to PWA system identification. At each iteration, a single optimization problem is solved, performing simultaneously the estimation of the partition of the regressor domain, the assignment of data points to submodels, and the estimation of the submodel parameters. A nice feature of the proposed approach is that at each iteration it provides a classification of the data points that is linearly separable by construction, while guaranteeing that the value of the prediction error criterion is non-increasing along the iterations. The optimization problem solved at each iteration is a mixed integer program, where the classification involves only a fixed number of data points close to the boundaries of the partition estimated at the previous iteration. This number can be tuned to control the computational burden of the mixed integer program to be solved. The proposed technique can be applied to tackle an identification problem from scratch, or to refine the solution provided by other suboptimal techniques. This is shown through an application to the pick-and-place machine data set.