Proactive cooperative consensus control for a class of human-in-the-loop multi-agent systems with human time-delays

In this study, we consider a class of human-in-the-loop (HiTL) multi-agent systems that divide agents into two parts: the nonautonomous agents controlled by human operators, and the autonomous agents. First, the human operators' models are incorporated into the multi-agent system for constructing an HiTL multi-agent system model. Next, the cooperative consensus control problem is explored for the HiTL multi-agent system, and a method is proposed that enables autonomous agents to proactively collaborate with human-controlled agents in order to mitigate the effects of human time-delays. We first obtain the consensus sufficient condition for the HiTL multi-agent system without human time-delays, and then give the method by only designing the autonomous agents' control gains to guarantee consensus. Subsequently, the delay-dependent consensus sufficient condition for the HiTL multi-agent system with human time-delays is also offered, and the method of controller design is updated for this case. Finally, a simulation experiment was designed, and the simulation results are presented to illustrate the effectiveness of the proposed methods.