Abstract: As an emerging computing paradigm, edge computing delegates data computing and processing tasks to the edge side close to users for execution, thereby avoiding the high latency caused by long-distance data transmission. With the increase of edge computing tasks, the problem of energy supply for edge computing centers has become a huge challenge. Using energy internet to power edge data centers is a feasible direction, but the generation of renewable energy and the energy consumption of edge data centers have strong uncertainty and randomness. Facing this challenge, this paper proposed a stochastic optimal robust control strategy based on Nash equilibrium. The controller maximizes the use of renewable energy to power edge data centers through optimal control, and also ensures that edge data centers perform data operations with the maximum possible working power. In addition, the controller also guarantees the stability of the bus frequency deviation in the presence of random disturbances from the environment. Considering that the two goals of optimal control and robust control might conflict with each other, this paper uses Nash equilibrium to achieve a balanced state between the two. Finally, this paper verifies the feasibility of the proposed method through numerical simulation.