network (DNN) models, and high computational complexity. Thus, the traditional power capping methods for CPU-based clusters or small-scale GPU devices do not apply to the GPU-based clusters handling DL tasks. This paper develops a cooperative distributed GPU power capping (CD-GPC) system for GPU-based clusters, aiming to minimize the training completion time of invoked DL tasks without exceeding the limited power budget. Specifically, we first design the frequency scaling (FS) approach using the online model estimation based on the recursive least square (RLS) method. This approach achieves the accurate tuning for DL task training time and power usage of GPU devices without needing offline profiling. Then, we formulate the proposed FS problem as a Lagrangian dual decomposition-based economic model predictive control (EMPC) problem for large-scale heterogeneous GPU clusters. We conduct both the NVIDIA GPU-based lab-scale real experiments and real job trace-based simulation experiments for performance evaluation. Experimental results validate that the proposed system improves the power capping accuracy to have a mean absolute error <1%, and reduces the deadline violation ratio of invoked DL tasks by 21.5% compared with other recent counterparts.