Piecewise Affine System Identification by Exploiting Sparsity in Tight-Dimensional Spaces

Identification of piecewise affine systems has been a major challenge in, e.g., modeling of hybrid systems. In this paper, we present an idea to exploit hidden sparsity in tight-dimensional representation spaces for piecewise affine system identification. More precisely, we propose a tight-dimensional linear transformation which reveals sparsity hidden in output signals of piecewise affine systems. This linear transformation is designed by applying a natural observation that most of output signals on neighboring data points are contained in special subspaces. Numerical examples show the effectiveness of the revealed sparsity for piecewise affine system identification.