A constrained clustering approach to bounded-error identification of switched and piecewise affine systems

This paper proposes a novel clustering-based approach to the bounded-error identification of switched and piecewise affine autoregressive exogenous systems. We address the problem of determining a minimal collection of linear-in-the-parameters models (called modes) fitting with a given accuracy $\eps$ a set of input-output data while complying with the switched or piecewise affine nature of the system. The problem is tackled by suitably clustering the data according to their preferences with respect to a pool of candidate models identified on subsets of the available data. The preference of a data point for a model is assessed based on the extent to which that model fits that data point and is set to zero if the fit is worse than $\eps$. A two-level clustering with outliers isolation is employed, first grouping data based on their preferences subject to suitable time/space adjacency conditions depending on the nature of the switching mechanism, and then collecting together non-adjacent clusters that can be described by the same mode. The performance of the proposed method is demonstrated via comparative numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.