Adaptive Consensus Algorithms for Matrix-Weighted Networks with Parametric Uncertainties

In this paper, we study the consensus problem for agents with parametric uncertainties interacting over matrix-weighted graphs. First, an adaptive matrix-weighted consensus algorithms for single-integrator agents is proposed and then extended to double- and higher-order integrator agents. Second, adaptive model-reference adaptive matrix-weighted consensus and its robustness are discussed. For each proposed consensus algorithm, conditions for the adaptive variables to converge to the uncertain parameters are also given. Finally, applications of the proposed consensus algorithms in displacement-based network localization and formation control are discussed and demonstrated by simulations.