Distributed Formation Control for a Class of Human-in-the-Loop Multiagent Systems

In this article, the distributed formation control problem for a class of human-in-the-loop (HiTL) multiagent systems (MASs) is studied. A hidden Markov jump MAS is employed to model the HiTL MAS, which integrates the human models, the MAS model, and their interactions. The HiTL MAS investigated in this article is composed of two parts: a leader without human in the control loop and a group of followers in which each follower is simultaneously controlled by a human operator and an automation. For each follower, a hidden Markov model is used for modeling the human behaviors in consideration of the random nature of human internal state (HIS) reasoning and the uncertainty from HIS observation. By means of a stochastic Lyapunov function, a necessary and sufficient condition is first developed in terms of the linear matrix inequalities (LMIs) to ensure the formation of the HiTL MAS in the mean-square sense. Then, an LMI approach to the human-assistance control design is proposed for the automations in the followers to guarantee the mean-square formation of the HiTL MAS. Finally, simulation results are presented to verify the effectiveness of the proposed methods.