Abstract: This study proposes two speed controllers based on a robust adaptive non-singular terminal sliding mode control approach for the cooperative adaptive cruise control problem in a connected and automated vehicular platoon. The delay-based spacing policy is adopted to guarantee that all vehicles in the platoon track the same target velocity profile at the same position while maintaining a predefined time gap. Factors such as nonlinear vehicle longitudinal dynamics, engine dynamics with time delay, undulating road profiles, parameter uncertainties, and external disturbances are considered in the system modeling and controller design. Different control objectives are assigned to the leading and following vehicles. Then, controllers consisting of a sliding mode controller with parameter adaptive laws based on the ego vehicle’s state deviation and linear coupled state errors, and a Smith predictor for time delay compensation are designed. Both inner stability and strong string stability are guaranteed in the case of nonlinear sliding manifolds. Finally, the effectiveness of the proposed controllers and the benefits of 44.73% shorter stabilization time, 11.20% less speed overshoot, and virtually zero steady-state inner vehicle distance deviation are illustrated in a simulation study of a seven-vehicle platoon cooperative adaptive cruise control and comparison experiments with a coupled sliding mode control approach.