Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems

Abstract-- We develop an interpolation-based framework for noisy linear systems with unknown system matrix with bounde d norm (implying bounded growth or non-increasing energy), and bounded process noise energy. The proposed approach characterizes all trajectories consistent with the measur ed 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 leverage d for safety verification and cost minimization. Ultimately, thi s work represents a preliminary step toward exploiting interpola tion conditions in data-driven control, offering a systematic w ay to characterize trajectories consistent with a dynamical sys tem within a given class and enabling their use in control design . Data-driven control has become a crucial aspect of modern control theory, offering powerful tools for system analysis and design [1].