Adaptive Control of Second-Order Safety-Critical Multiagent Systems With Nonlinear Dynamics

In this article, we propose a distributed adaptive control architecture for leader-following consensus of uncertain multiagent systems with second-order nonlinear dynamics. A nonlinear reference model system captures an ideal behavior of the agents for the leader-following consensus problem. We design a modified nonlinear reference model system and propose a distributed model reference adaptive control architecture to suppress the effects of system uncertainties without a strict knowledge of their magnitude and rate upper bounds. Consequently, each agent evolves within a (possibly different) prescribed distance from the corresponding modified reference system trajectories. Based on an input-to-state stability analysis, it is shown that the trajectories of the modified reference model system can get arbitrarily close to the trajectories of the ideal reference model system. As a result, the trajectories of the agents evolve within a user-specified prescribed distance from their ideal system trajectories, satisfying the safety constraints. The key feature of the presented control architecture in this article is the elimination of the
ad hoc
tuning process for the adaptation rate that is conventionally required in model reference adaptive control systems to ensure safety. An illustrative numerical example finally demonstrates the efficacy of the proposed distributed adaptive control architecture.