Unveiling system controllability from noisy data by harnessing network structures
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- In recent years, data-driven control has gained prominence as an alternative to traditional model-based strategies, particularly in contexts where constructing accurate system models is difficult. Controllability remains a cornerstone of control theory, as it determines the feasibility of designing effective control inputs. This work addresses the problem of assessing controllability from noisy input–state trajectory data, aiming to bridge the gap between theoretical guarantees and the challenges posed by real-world noise-affected systems. The study begins with a review of the literature on data-driven control, system identification, and structural analysis, with an emphasis on the various definitions of controllability. Special attention is given to the data-informativity framework, which allows controllability to be tested directly from measured data. However, both theoretical analysis and numerical evidence highlight a key limitation of this approach: its lack of robustness in the presence of noise. To address this issue, a hybrid method is introduced. Rather than applying controllability tests directly to noisy measurements, the structural sparsity of the system is first inferred using either hard thresholding or LASSO regression. The resulting estimate is then analyzed using structural controllability theory. Simulations conducted on both random and deliberately constructed systems show that this two-step approach improves robustness significantly, yielding high accuracy even under non-negligible noise. Overall, this framework offers a practical and noise-resilient alternative for data-driven controllability assessment, and suggests new research directions at the intersection of structural inference, noisy data and controllability.