  Data-driven predictive control promises model-free wave-dampening strategies
for Connected and Autonomous Vehicles (CAVs) in mixed traffic flow. However,
its performance relies on data quality, which suffers from unknown noise and
disturbances.This paper introduces a Robust Data-EnablEd Predictive Leading
Cruise Control (RDeeP-LCC) method based on reachability analysis, aiming to
achieve safe and optimal CAV control under bounded process noise and external
disturbances. Precisely, the matrix zonotope set technique and Willems'
Fundamental Lemma are employed to derive the over-approximated system dynamics
directly from data, and a data-driven feedback control technique is utilized to
obtain an additional feedback input for stability. We decouple the mixed
platoon into an error system and a nominal system, where the error system
provides data-driven reachability sets for the enhanced safety constraints in
the nominal system. Finally, a data-driven predictive control framework is
formulated in a tube-based control manner for robustness guarantees. Nonlinear
simulations with noise-corrupted data demonstrate that the proposed method
outperforms baseline methods in mitigating traffic waves.
