Distributed control of multi-agent systems with major agents and Markov parameters

In this paper, we investigate distributed control of the multi-agent systems with a major agent and a large number of minor agents in Markovian environment, where agents are coupled by the quadratic tracking indices with random parameters. The major agent has salient impact on others. Each minor agent merely has tiny influence, while the average effect of all the minor agents is not negligible, which plays a significant role in the evolution and performance index of each agent. Besides the state of the major agent, each minor agent can only access to the information of its state and parameters. Based on the mean field theory, a set of distributed control laws is designed. By the probability limit theory, the uniform stability of the closed-loop systems and the upper bound of the corresponding index values are obtained.