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Given the aging infrastructure and the anticipated growing number of highway work zones in the U.S.A., it is important to investigate work zone merge control, which is critical for improving work zone safety and capacity. This paper proposes and evaluates a novel highway work zone merge control strategy based on cooperative driving behavior enabled by artificial intelligence. The proposed method assumes that all vehicles are fully automated, connected, and cooperative. It inserts two metering zones in the open lane to make space for merging vehicles in the closed lane. In addition, each vehicle in the closed lane learns how to adjust its longitudinal position optimally to find a safe gap in the open lane using an off-policy soft actor critic reinforcement learning (RL) algorithm, considering its surrounding traffic conditions. The learning results are captured in convolutional neural networks and used to control individual vehicles in the testing phase. By adding the metering zones and taking the locations, speeds, and accelerations of surrounding vehicles into account, cooperation among vehicles is implicitly considered. This RL-based model is trained and evaluated using a microscopic traffic simulator. The results show that this cooperative RL-based merge control significantly outperforms popular strategies such as late merge and early merge in terms of both mobility and safety measures. It also performs better than a strategy assuming all vehicles are equipped with cooperative adaptive cruise control.