Adaptive Output Formation-Tracking of Heterogeneous Multi-Agent Systems Using Time-Varying $\mathcal {L}_{2}$ -Gain Design

This letter investigates the adaptive output formation-tracking problem of general linear heterogeneous multi-agent systems (MAS). The leader's dynamics are only known to its neighboring followers. All followers are assumed to be non-introspective, i.e., they have no self-knowledge, and only receive relative output information from neighbors. First, both the desired formation and the formation reference, i.e., the leader's output trajectory, can be time-varying. Then, we provide the sufficient conditions for the existence of a distributed controller to guarantee the adaptive time-varying output formation-tracking of heterogeneous MAS with an unknown leader. Finally, we develop a time-varying L
₂
-gain design problem to achieve the adaptive output formation-tracking. The local design procedures are rigorously derived in terms of solving novel time-varying matrix Riccati differential equations.