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This paper presents an advanced scheduling approach tailored for real-time tasks executing on heterogeneous computing platforms common in modern networked control systems and cyber-physical systems, which encompass both multicore processors and multiple identical GPUs. Building on the server-based scheduling approach for single-GPU systems, our approach extends these principles to multi-GPU environments, addressing the complexities associated with managing multiple shared GPU resources. Introducing a dedicated server task to handle GPU requests in a priority-driven manner avoids the limitations of busy waiting and long priority inversions often encountered in traditional lock-based scheduling approaches. The paper also develops the worst-case response-time analysis of tasks that are scheduled using the proposed scheduling approach on these systems. The evaluation results demonstrate that our approach achieves comparable performance to the single-GPU server-based approach while delivering significant performance improvements over the traditional lock-based approaches, especially in improving the schedulability rate of task sets in multicore and multi-GPU systems. Compared to existing synchronization-based approaches, the proposed framework avoids busy-waiting and reduces priority inversion while enabling analyzable GPU access in multi-GPU systems. In addition, the proposed response-time analysis explicitly captures GPU blocking and interference.