Robust Data-Driven Control of LPV Systems With Safety Guarantees

Direct data-driven control approaches based on the fundamental lemma by Willems et al. offer a promising alternative to model-based approaches by bypassing explicit system identification. However, their extension to linear parameter-varying (LPV) systems presents challenges due to the scheduling-dependent dynamics and the need for accounting for safety constraints. This paper proposes a direct data-driven control framework for unknown LPV systems that guarantees pointwise-in-time safety constraints via semi-definite programming (SDP). By leveraging input-state-scheduling data and employing Petersen's lemma, we develop a tractable parameterization of admissible LPV trajectories and reformulate state constraints as conditions on positively invariant (PI) sets. The framework is extended to handle both offline and online process disturbance, with a reduced-complexity SDP formulation introduced for disturbance with known spectral characteristics. Numerical results validate the effectiveness and robustness of the proposed approach.