Fully Distributed Fault-Tolerant Consensus Protocols for Lipschitz Nonlinear Multi-Agent Systems

In this paper, we investigate the fault-tolerant consensus problems for multi-agent systems with actuator faults. Based on the relative state information, fully distributed adaptive protocols are designed for these agents described by Lipschitz nonlinear dynamics under leaderless and leader-follower communication structures. As the special case, for linear multi-agent systems, fault-tolerant consensus problems are also solved with the proposed protocols. First, for the leaderless multi-agent systems, all agents reach an agreement on a common value with undirected connected communication graphs. Second, for the leader-follower multi-agent systems, in which the state of the leader is only available to a subset of the followers, the state of each follower converges to the state of the leader, asymptotically. A distinctive feature of this paper is that the adaptive protocols here are independent of the eigenvalues of the Laplacian matrix associated with the whole communication graph, which means the protocols can be implemented by each agent in a fully distributed fashion. Simulation examples are provided to illustrate the theoretical results.