To overcome the limitations of existing centralized approaches for particle accelerator control, this paper presents a distributed multi-agent framework based on a large-scale language model (LLM). Each agent controls an individual component of the accelerator, communicates with each other, and handles high-level tasks. The system aims to be self-improving, improving through experience and human feedback, emphasizing the importance of data labeling and expert guidance through human intervention. Three examples demonstrate the feasibility of the proposed architecture.