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Real-time control of a fleet of Connected and Automated Vehicles (CAV) for Cooperative Adaptive Cruise Control (CACC) is a challenging problem concerning time delays (from sensing, communication, and computation) and actuator lag. This paper proposes a real-time predictive distributed CACC control framework that addresses time delays and actuator lag issues in the real-time networked control systems. We first formulate a Kalman Filter-based real-time current driving state prediction model to provide more accurate initial conditions for the distributed CACC controller by compensating time delays using sensing data from multi-rate onboard sensors (e.g., Radar, GPS, wheel speed, and accelerometer), and status-sharing and intent-sharing data in BSM via V2V communication. We solve the prediction model using a sequential Kalman Filter update process for multi-rate sensing data to improve computational efficiency. We propose a real-time distributed MPC-based CACC controller with actuator lag and intent-sharing information for each CAV with the delay-compensated predicted current driving states as initial conditions. We implement the real-time predictive distributed CACC control algorithms and conduct numerical analyses to demonstrate the benefits of intent-sharing-based distributed computing, delay compensation, and actuator lag consideration on string stability under various traffic dynamics.