Real-time scheduling algorithms proposed in the literature are often based on worst-case estimates of task parameters. The performance of an open-loop scheme can be degraded significantly if there are uncertainties in task parameters, such as the execution times of the tasks. Therefore, to cope with such a situation, a closed-loop scheme, where feedback is exploited to adjust the system parameters, can be applied. We propose an optimal control framework that takes advantage of feeding back information of finished tasks to solve a real-time multiprocessor scheduling problem with uncertainty in task execution times, with the objective of minimizing the total energy consumption. Specifically, we propose a linear programming based algorithm to solve a workload partitioning problem and adopt McNaughton's wrap around algorithm to find the task execution order. The simulation results illustrate that our feedback scheduling algorithm can save energy by as much as 40% compared to an open-loop method for two processor models, i.e. a PowerPC 405LP and an XScale processor.