Safety-Critical Containment Control for Multi-Agent Systems With Communication Delays

Recently, the containment control for multi-agent systems (MASs) with communication delays has been studied. However, in these existing results, the assumptions for delays are too strong, leading to deviations from reality; moreover, safety is rarely considered, especially under a surging number of collision threats and the state constraint. In this work, we focus on the containment control for MASs with nonuniform time-varying communication delays; the formation configuration is extended to a dynamic one with time-varying velocity, and the model of agents is extended to the Euler-Lagrange (EL) model with uncertainty. We present sufficient conditions for containment control in the above case by utilizing the Lyapunov-Krasovskii function and the linear matrix inequalities (LMIs). Moreover, we propose a robust control barrier function (CBF)-based obstacle avoidance approach that ensures MAS safety through optimal control, thus better synthesizing the conflict between safety and the original control goals. In addition, considering that model uncertainty can adversely affect CBFs, we propose an observer with a quantified error to provide CBFs with robustness against uncertainty. Finally, simulation results demonstrate the validity of the proposed method.