Data-Driven Synthesis of Robust Positively Invariant Sets from Noisy Data
This work addresses robust control design for systems with unknown dynamics and noisy data, which is incremental as it builds on existing tube-based methods by incorporating data-driven synthesis.
The paper tackles the problem of constructing robust positively invariant (RPI) tube sets from noisy data for unknown linear time-invariant systems, enabling direct use in tube-based predictive control, with numerical examples quantifying the conservatism introduced by data noise and certification steps.
This paper develops a method to construct robust positively invariant (RPI) tube sets from finite noisy input-state data of an unknown linear time-invariant (LTI) system, yielding tubes that can be directly embedded in tube-based robust data-driven predictive control. Data-consistency uncertainty sets are constructed under process/measurement noise with polytopic/ellipsoidal bounds. In the measurement-noise case, we provide a deterministic and data-consistent procedure to certify the induced residual bound from data. Based on these sets, a robustly stabilizing state-feedback gain is certified via a common quadratic contraction, which in turn enables constructive polyhedral/ellipsoidal RPI tube computation. Numerical examples quantify the conservatism induced by noisy data and the employed certification step.