Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems
This work provides a systematic framework for data-driven control in noisy linear systems, representing a preliminary step toward exploiting interpolation conditions in this domain.
The authors tackled the problem of characterizing all possible trajectories consistent with measured data and prior bounds in noisy linear systems, enabling data-consistency verification, inference, and one-step ahead prediction for applications like safety verification and cost minimization.
We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounded norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measured data and these prior bounds in a purely data-driven manner. This characterization enables data-consistency verification, inference, and one-step ahead prediction, which can be leveraged for safety verification and cost minimization. Ultimately, this work represents a preliminary step toward exploiting interpolation conditions in data-driven control, offering a systematic way to characterize trajectories consistent with a dynamical system within a given class and enabling their use in control design.