Connected automated vehicle (CAV) platoon control is becoming increasingly prevalent because of its unique advantages in reducing fuel consumption and improving traffic efficiency. A novel control framework for CAV platoon control is designed in this article. First, a model predictive control (MPC)-based method is proposed to obtain the optimal velocity of the whole platoon, in which both reducing fuel consumption and improving transport efficiency are taken into account in the optimization process. Then, a distributed adaptive triple-step nonlinear control strategy is investigated from the perspective of multiagent system control. The adaptive performance of the control strategy can guarantee the string stability of the CAV platoon under the premise of the existence of dynamic uncertainties. Various simulation conditions with heterogeneous dynamic disturbances are designed to validate the proposed control strategy, and the results show that the proposed control strategy can be robust to dynamic disturbances while ensuring the string stability of the CAV platoon.