In hard-real-time environment, scheduling periodic tasks upon multiprocessors is one of the most popular problems where uniform multiprocessor scheduling is a well-known one. In this platform, execution time of each task in one processor is proportional to the computing capacity of this processor. From previous works, we know there are only approximate feasible solutions for on-line scheduling on uniform multiprocessors. In this paper, with task migration, we first present a novel model called T-L er plane to describe the behavior of tasks and processors, and two optimal on-line algorithms based on T-L er plane to schedule real-time tasks with dynamic-priority assignment on uniform multiprocessors. To make it practical and to reduce context switches, we also present a polynomial-time algorithm to bound the times of rescheduling in a T-L er plane. Since task migration is easier in SOC multicore processors, our result might be applicable and adapted to many asymmetric multicore platforms.