Accelerated consensus to accurate average in multi-agent networks via state prediction

This paper considers the double-integrator consensus speeding up problem for multi-agent networks (MANs) asymptotically achieving distributed weighted average. First, basic theoretical analysis is carried out and several necessary and sufficient conditions are derived to ensure convergence to weighted average for both directed and undirected networks, but the convergence is generally slow. In order to improve the rate of convergence, an approach is proposed to accelerate consensus by utilizing a linear predictor to predict future node state on the basis of the current and outdated node state. The local iterative algorithm then becomes a convex weighted sum of the original consensus update iteration and the prediction, which allows for a significant increase in the rate of convergence towards weighted average consensus because redundant sates are bypassed. Additionally, the feasible region of mixing parameter and optimal mixing parameter are determined for undirected networks. It is worth pointing out that the accelerated framework has tapped the maximum potential to the utmost, from both the current and outdated state stored in the memory, to improve the rate of convergence without increasing the computational and memorial burden. Finally, a simulation example is provided to demonstrate the effectiveness of our theoretical results.