Distributed tracking of nonlinear multi-agent systems with unstable dynamics

This paper addresses the problem of distributed output tracking for a class of nonlinear multi-agent systems whose linearized systems may have unstable modes. For the case where the graph topology is directed and the leader is the neighbor of only a small portion of followers, distributed tracking control laws are designed. By using the algebra graph theory, it is shown that all the states of the closed-loop system are bounded, and the tracking errors can be tuned to arbitrarily small. Finally, the design procedure is applied to underactuated unstable mechanical multi-agent systems, from which the efficiency of the tracking controllers is demonstrated.