Closed-loop Reference Model based Distributed Model Reference Adaptive Control for Multi-agent Systems

This paper confluences ideas from distributed model reference adaptive control (MRAC) architecture for multi-agent systems and closed-loop reference model (CRM) based MRAC algorithm. The concept of CRM is recently proposed in literature for single-agent MRAC problems, where the reference model (leader) gets feedback from the plant (agent/follower) to facilitate improved transient performance. This work coins the concept of CRM based distributed MRAC, where it is assumed that the leader/reference model is connected only to a subset of followers and incorporates feedback from them in a multi-agent setting. Distributed parameter estimator and controller are designed, which incorporate inter-agent cooperation via communication over a bi-directional graph. The leader state and the time-varying leader input (also known as reference input in MRAC literature) are only accessible to its neighbours. A novel distributed dynamic surface control (DSC)-like strategy is invoked for each follower to cooperatively estimate the unknown reference input required for control design. Simulation results dictate that the proposed closed-loop leader based formulation leads to better transient performance as compared to the status quo and also enables the use of high gain tuners for adaptive update law. As far as the authors are aware, this is the first work which introduces a distributed protocol of CRM-MRAC for multi-agent systems (CRM-DMRAC) with rigorous Lyapunov analysis.