Research on stochastic process modeling and optimal control algorithm in multi-agent system

Aiming at the uncertainties of multi-agent system (MAS) in complex environment, such as communication randomness, environmental randomness and sensor noise, this paper proposes a distributed optimal control framework based on stochastic process modeling. Firstly, a distributed model considering communication link reliability, environmental interference and sensor noise is constructed, in which communication link reliability is modeled by Markov chain, environmental randomness is described by stochastic differential equation, and sensor noise is described by mixed model. Then, the complexity of large-scale MAS is simplified by using the mean field theory, and a distributed optimal control algorithm based on random gradient descent is designed. By introducing the H∞ robust control correction term, the dynamic balance between local and global optima is realized, and the system's resistance to random interference is enhanced. Through the typical scene experiments of UAV formation control and smart grid load balancing, it is verified that the proposed algorithm has obvious advantages over traditional methods in convergence speed, anti-interference ability and steady-state accuracy, and it shows higher stability and efficiency in large-scale systems, which provides theoretical support and practical guidance for efficient cooperation and stable operation of multi-agent systems in complex environments.