Leader-following consensus of a class of heterogeneous uncertain multi-agent systems with a distributed model reference adaptive control law

This paper considers the leader-following consensus problem of a multi-agent system whose agents have heterogeneous uncertain dynamics in homogeneous state dimensions. Each agent utilizes a distributed model reference adaptive control (MRAC) law to deal with uncertainties. The nominal part of the MRAC is a distributed static state feedback control law. The reference model is the leader-following consensus problem of reference agents with homogeneous linear time-invariant dynamics. This problem becomes an N-player graphical differential game under a given cost function. The reference agents utilize distributed static state feedback controllers that constitute a Nash equilibrium solution to the graphical differential game. This paper provides the conditions for the distributed MRAC to guarantee that each agent asymptotically tracks the corresponding reference agent; consequently, the multi-agent system solves the leader-following consensus problem as the reference model does. These conditions yield a straightforward design method for the MRAC. A numerical example demonstrates an application of the proposed approach to a multi-robot system with nonlinear dynamics.