Leader-Following Consensus of Discrete-Time Multi-Agent Systems via Distributed Model Reference Adaptive Control

In this paper, we study the leader-following adaptive tracking control problem for a class of discrete-time linear uncertain multi-agent systems (MAS). To deal with this problem, we develop a distributed model reference adaptive control framework, which extends the classical MRAC method to MAS scenario. Taking the reference model system as the leader agent, we first develop a nominal distributed controller only using local neighboring information, where the ideal controller parameters are derived by a matching equation and neighboring system parameters. Based on the nominal controller structure, a distributed adaptive control law is developed by introducing a parameter update law for the estimated controller parameters. Further, to eliminate the requirement for the prior knowledge of control gains, we devise a modified distributed adaptive control law, which incorporate the implicit control gain estimate into the controller structure, thus deriving a linear local estimation error equation. Thus, a gradient based parameter update law could be designed without any prior parameter information. Notably, the leader agent is also with paraemter uncertainty and the modification does not rely on common Nussbaum function. Asymptotical leader-following output tracking is achieved under the proposed distributed adaptive control strategies. The simulation results also demonstrate the theoretical findings.