Distributed adaptive consensus protocol with Laplacian eigenvalues estimation

This paper addresses distributed consensus problem for multi-agent systems with general linear time-invariant dynamics and undirected connected communication graphs. A distributed adaptive consensus protocol is found to solve problems of existing adaptive consensus protocols related to different, generally large and possibly unbounded coupling gains. This protocol guarantees ultimate boundedness under all conditions, however for an asymptotic stability, a proper estimation of reference values for coupling gains is required. Here, we propose an algorithm for the estimation of the coupling gain reference. The algorithm is based on a distributed estimation of the Laplacian eigenvalues. In comparison to the previously proposed algorithm based on the interval halving method, this algorithm offers robustness to change of the network topology. In addition, it decouples the estimation from the consensus protocol, hence it does not influence stability properties of the adaptive consensus protocol.