A novel strategy to enhance string stability of autonomous vehicles with sensor delay and actuator lag is proposed based on a model predictive control framework. To compensate sensor delay, the approach entails estimating the (unknown) system state at the current time using the system state in a previous time, the applied control history and a system dynamics model. The actuator lag is compensated by including the lag in the state prediction model. The mathematical framework shows that without the anticipation strategy, sensor delay leads to a worse estimate of the initial condition for the optimal control problem and actuator lag increases the mismatch between the system state prediction model and the actual system behaviour. Simulation verified that sensor delay and actuator lag degrade string stability of platoons. The proposed anticipatory control strategy shows clear benefits in improving autonomous vehicle string stability and hence has potential to enhance traffic flow stability.