Parameter Robustness in Data-Driven Estimation of Dynamical Systems

We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main contribution of this paper is the development of a novel robustness metric for estimation of parametrized linear dynamical systems with and without control actions. For the computation of this metric, we delineate the uncertainty contributions arising from control actions, system dynamics, and initial conditions. Furthermore, to validate our theoretical findings, we establish connections between these new results and the existing literature on the robustness of model reduction. This work provides guidance for selecting estimation methods based on tolerable levels of parametric uncertainty and paves the way for new cost functions in data-driven estimation that reward sensitivity to a desired subset of parameters while penalizing others.