To address the multiple constraints faced during the operation of electric multiple unit (EMU), including aggregated disturbances (unknown time-varying disturbances, additional resistance, inter-unit coupling forces, and basic resistance), input saturation, and limited buffer stroke, a distributed finite-time prescribed performance robust consensus controller based on multi-agent theory is proposed in combination with artificial potential function. First, according to the different working ranges of the buffer stroke, a new judging mechanism of potential force is proposed, and an adaptive repulsive and attractive potential functions are constructed using the logarithmic function. Second, combining cosine function and exponential function, a novel finite-time prescribed performance function is designed, which effectively constrains the convergence boundary and settling time of the tracking errors of each power unit, thus achieving predefined dynamic performance. In addition, a fixed-time disturbance observer and a filter-based compensation approach are introduced to handle the effects of aggregated disturbances and input saturation. Compared with existing methods, the main advantage of this study is that the control performance of the EMU system can be guaranteed in advance, while simultaneously ensuring practical finite-time stability, string stability and safe inter-unit spacing, and providing stronger robustness. Finally, with the CRH380A high-speed EMU as the research object, both theoretical analysis and numerical simulations are conducted to verify the effectiveness and feasibility of the proposed control method.