Design of Robust Dynamic Average Consensus Estimators

The block diagram for a general average consensus estimator is developed and we show how this can be used to easily identify properties of the estimator. This structure is then used to design average consensus estimators which achieve exact average consensus for constant inputs, are robust to initial conditions and switching graph topologies, and are internally stable. Additionally, the estimators have the optimal worstcase asymptotic convergence rate over the set of connected undirected graphs whose weighted Laplacian matrices have nonzero eigenvalues in a known interval [lambda(min), lambda(max)]. Two designs are presented. The first is a modification of the polynomial filter estimator proposed by Kokiopoulou and Frossard [1] which is the optimal estimator having only one state variable. The proposed design is robust to initial conditions, but not robust to switching graph topologies. The second design uses root locus techniques to obtain higher-dimensional estimators in closed-form which are robust to both initial conditions and switching graph topologies. Plots of the worst-case asymptotic convergence factor of each estimator are given as a function of the ratio lambda(min)/lambda(max).