A Robust Algorithm for Online Switched System Identification

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.

Behavioral uncertainty quantification for data-driven control

“…Namely, we determine the mode of a switched autoregressive exogenous (SARX) system directly from data for the purpose of data-driven control. Consider a SARX system [36] with 2 modes given by…”

Behavioral uncertainty quantification for data-driven control

“…Namely, we determine the mode of a switched autoregressive exogenous (SARX) system directly from data for the purpose of data-driven control. Consider a SARX system [33] with 2 modes given by…”

Learning event-driven switched linear systems

“…In [33] the author studies online identification of switched systems as an extension of the offline algebraic method (see (a) above). The works [5,18,14] employ two-step procedures for online identification of switched systems. First, candidate estimates for each subsystem are built, and second, at every time, the active subsystem is determined by assigning the data to one of the candidates according to some criteria and the estimates of the candidates are updated.…”

“…In particular, [5] employs prior or posterior residual error for the identification of active subsystems and recursive least squares for updating the candidate estimates, while [18] employs minimization of prior residual error for the identification of active subsystems and a modified outer bounding ellipsoid algorithm for the updation of candidate estimates. The residual error approach for the identification of active subsystem at every time step is modified to a robust version by incorporating an upper bound on estimation error in [14]. The authors employ a randomized Kaczmaz algorithm and normalized least mean squares towards updating the candidate estimates of the subsystems parameters.…”