Analysis of the least sum-of-minimums estimator for switched systems

TL;DR

This paper analyzes a complex nonconvex estimator for switched systems, focusing on its fundamental properties and how data influences its performance, independent of computational issues.

Contribution

It provides a theoretical analysis of the least sum-of-minimums estimator, highlighting its key properties and data-dependent performance aspects.

Findings

Uniqueness conditions for the estimator's solution

Boundedness of estimation error regardless of computation

Influence of data properties on estimator performance

Abstract

This paper considers a particular parameter estimator for switched systems and analyzes its properties. The estimator in question is defined as the map from the data set 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 sub-functions. This is a hard nonconvex problem. The paper 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.