A Robust Algorithm for Online Switched System Identification

TL;DR

This paper introduces a robust online algorithm for identifying switched systems that effectively estimates subsystem parameters and switching sequences with theoretical guarantees and strong empirical performance.

Contribution

A novel two-step online algorithm for switched system identification that improves robustness and provides theoretical convergence guarantees.

Findings

Algorithm outperforms existing methods in simulations.

Effective even with random initialization.

Provides theoretical guarantees on local convergence.

Abstract

In this paper, we consider the problem of online identification of Switched AutoRegressive eXogenous (SARX) systems, where the goal is to estimate the parameters of each subsystem and identify the switching sequence as data are obtained in a streaming fashion. Previous works in this area are sensitive to initialization and lack theoretical guarantees. We overcome these drawbacks with our two-step algorithm: (i) every time we receive new data, we first assign this data to one candidate subsystem based on a novel robust criterion that incorporates both the residual error and an upper bound of subsystem estimation error, and (ii) we use a randomized algorithm to update the parameter estimate of chosen candidate. We provide a theoretical guarantee on the local convergence of our algorithm. Though our theory only guarantees convergence with a good initialization, simulation results show that even with random initialization, our algorithm still has excellent performance. Finally, we show, through simulations, that our algorithm outperforms existing methods and exhibits robust performance.