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Signalized intersections play an important role in transportation efficiency and vehicle fuel economy in urban areas. This paper proposes a cooperative method of traffic signal control and vehicle speed optimization for connected automated vehicles, which optimizes the traffic signal timing and vehicles' speed trajectories at the same time. The method consists of two levels, i.e., roadside traffic signal optimization and onboard vehicle speed control. The former calculates the optimal traffic signal timing and vehicles' arrival time to minimize the total travel time of all vehicles; the latter optimizes the engine power and brake force to minimize the fuel consumption of individual vehicles. The enumeration method and the pseudospectral method are applied in roadside and onboard optimization, respectively. Simulation studies are conducted to compare the proposed method with benchmark methods. The results show …