Urban intersection management affects traffic safety and flow. Particularly with the increasing presence of Connected Autonomous Vehicle (CAV), pedestrians, and cyclists, inefficient control can lead to congestion, delays, and an increased risk of accidents. Data communication failures due to physical obstacles, interference, network issues, or faulty sensors can create information gaps that negatively impact management solutions. We present an intersection management system for CAVs that relies on continuous data communication between vehicles and infrastructure. The system performs conflict analysis to identify potential collisions while dynamically adjusting vehicle speeds. To address missing information, we incorporate data imputation usingPiecewise Cubic Hermite Interpolating Polynomial (PCHIP), a method for smooth time series interpolation method. Simulation results demonstrate that Dynamic Adaptive Intersection Control System (DAICS) sustains high performance under data loss scenarios, reducing average travel time by 68.4% compared to the baseline algorithm, Intersection Management for Autonomous Vehicles (IMAV).