Analysis of the Least Sum-of-Minimums Estimator for Switched Systems

This article considers a particular parameter estimator for switched systems and analyzes its properties. The estimator in question is defined as the map from the dataset to the solution set of an optimization problem where the to-be-optimized cost function is a sum of pointwise infima over a finite set of subfunctions. This is a hard nonconvex problem. The article studies some fundamental properties of this problem such as uniqueness of the solution or boundedness of the estimation error regardless of computational considerations. The interest of the analysis is to lay out the main influential properties of the data on the performance of this (ideal) estimator.