Distributed Average Tracking With Incomplete Measurement Under a Weight-Unbalanced Digraph

Abstract

During the implementation of a cooperative algorithm, information about the agents’ velocity may be unavailable due to the space constraint and availability of sensors. Thus, it gives rise to the design of distributed average tracking (DAT) algorithms without using agents’ velocity measurements. These are denoted as velocity-free DAT problems. The existing literature has addressed such problems in the presence of an undirected graph for the reference signals with bounded position, velocity, and acceleration differences. We propose a velocity-free DAT algorithm under a weight-unbalanced strongly-connected digraph that represents the most general network structure for achieving DAT. Additionally, the proposed algorithm works for a broader range of time-varying references, having bounded acceleration differences among themselves. Linear stability theory is used to establish uniform ultimate boundedness of the errors for bounded acceleration differences. Asymptotic convergence of the errors is guaranteed for converging acceleration differences. Unlike the existing works, our DAT algorithm does not need any update law for the gains. Thus, the approach is computationally efficient. Numerical simulations with the comparison with the state-of-the-art demonstrate the performance of our algorithm over a wider range of time-varying references under weight-unbalanced graph.