  Rapid transitions are important for quick response of consensus-based,
multi-agent networks to external stimuli. While high-gain can increase response
speed, potential instability tends to limit the maximum possible gain, and
therefore, limits the maximum convergence rate to consensus during transitions.
Since the update law for multi-agent networks with symmetric graphs can be
considered as the gradient of its Laplacian-potential function, Nesterov-type
accelerated-gradient approaches from optimization theory, can further improve
the convergence rate of such networks. An advantage of the accelerated-gradient
approach is that it can be implemented using accelerated
delayed-self-reinforcement (A-DSR), which does not require new information from
the network nor modifications in the network connectivity. However, the
accelerated-gradient approach is not directly applicable to general directed
graphs since the update law is not the gradient of the Laplacian-potential
function. The main contribution of this work is to extend the
accelerated-gradient approach to general directed graph networks, without
requiring the graph to be strongly connected. Additionally, while both the
momentum term and outdated-feedback term in the accelerated-gradient approach
are important in general, it is shown that the momentum term alone is
sufficient to achieve balanced robustness and rapid transitions without
oscillations in the dominant mode, for networks whose graph Laplacians have
real spectrum. Simulation results are presented to illustrate the performance
improvement with the proposed Robust A-DSR of 40% in structural robustness and
50% in convergence rate to consensus, when compared to the case without the
A-DSR. Moreover, experimental results are presented that show a similar 37%
faster convergence with the Robust A-DSR when compared to the case without the
A-DSR.
