Online Coreset Selection for Learning Dynamic Systems

TL;DR

This paper introduces an online coreset selection method for dynamic system identification that enhances data efficiency and guarantees convergence, even with disturbances and mismatched bounds, demonstrated through simulations.

Contribution

It develops a novel geometric selection criterion for online coreset construction with theoretical guarantees and extensions to nonlinear systems and noise.

Findings

Feasible set volume converges to zero under persistent excitation.

Explicit bounds on identification error with disturbance mismatch.

Effective data reduction demonstrated in simulations.

Abstract

With the increasing availability of streaming data in dynamic systems, a critical challenge in data-driven modeling for control is how to efficiently select informative data to characterize system dynamics. In this work, we develop an online coreset selection method for set-membership identification in the presence of process disturbances, improving data efficiency while preserving convergence guarantees. Specifically, we derive a stacked polyhedral representation that over-approximates the feasible parameter set. Based on this representation, we propose a geometric selection criterion that retains a data point only if it induces a sufficient contraction of the feasible set. Theoretically, the feasible-set volume is shown to converge to zero almost surely under persistently exciting data and a tight disturbance bound. When the disturbance bound is mismatched, an explicit Hausdorff-distance bound is derived to quantify the resulting identification error. In addition, an upper bound on the expected coreset size is established and extensions to nonlinear systems with linear-in-the-parameter structures and to bounded measurement noise are discussed. The effectiveness of the proposed method is demonstrated through comprehensive simulation studies.