Distributed adaptive consensus protocol with decaying gains

Abstract

SummaryThis article brings a distributed adaptive protocol for consensus and synchronization in multiagent systems on directed communication networks. Agents are modeled as general linear time‐invariant systems. The proposed protocol introduces a novel adaptation scheme allowing control coupling gains to decay to their reference values. This approach improves upon existing adaptive consensus protocols which may result in overly large or even unbounded coupling gains. The protocol design in this article does not rely on any centralized information; hence it is distributed. Nevertheless, the price to pay for this is the need to estimate those reference values. Convergence of the overall network dynamics is guaranteed for correctly estimated references; otherwise, the trajectory of the system is only uniformly ultimately bounded. Two estimation algorithms are proposed: one based on the interval‐halving method and the other based on a distributed estimation of Laplacian eigenvalues. Numerical simulations validate the proposed approach.