Robust Data‐Driven Control of LPV Systems With Safety Guarantees

ABSTRACT 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.