This study is devoted to developing a platoon-based cooperative lane-change control (PB-CLC). It coordinates the trajectories of a CAV platoon under a platoon-centered platooning control to accommodate the CAV lane-change requests from its adjacent lane, aiming to reduce the negative traffic impacts on the platoon resulting from lane-change maneuvers, on the premise of ensuring CAVs’ safety and mobility. Mathematically, the PB-CLC control is established using a hybrid model predictive control (MPC) system. The hybrid MPC system involves an MPC-based mixed integer nonlinear programming optimizer (MINLP-MPC) for optimal lane-change decisions, which considers multiple objectives such as traffic smoothness, driving comfort and lane-change response promptness subject to vehicle dynamics and safety constraints. To ensure the feasible lane-change, this study investigates and provides a lower bound of the lane-change time window by analyzing the MINLP-MPC model feasibility. Apart from the optimal lane-change decision consideration, the hybrid MPC system is well designed to ensure the control continuity and smoothness. In particular, the hybrid MPC system control feasibility and stability are proved to enable the platoon's back-and-forth state switchings between car-following and lane-change accommodation states. Next, we developed a machine learning aided distributed branch and bound algorithm (ML-DBB) to solve the MINLP-MPC model within a control sampling time interval (< 1 second). Specifically, built upon computer simulation and the c-LHS sampling technique, supervised machine learning models are developed offline to predict a reduced solution space of the integer variables, which is further integrated into the distributed branch and bound method to solve the MINLP-MPC model efficiently online. Extensive numerical experiments validate the effectiveness and applicability of the ML-DBB algorithm and the PB-CLC control.