Rapid Transitions with Robust Accelerated Delayed Self Reinforcement for Consensus-based Multi Agent Networks.
Anuj Kumar Tiwari, Santosh Devasia · arXiv (Cornell University) · 2020
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 non-symmetric graphs since the update law is not the gradient of the Laplacian-potential function. The main contributions of this work are to (i) extend the accelerated-gradient approach to general graph networks (whose Laplacians have real spectrum) using DSR, and (ii) develop analytical design criteria for a Robust A-DSR approach that maximizes both structural robustness and transition speed. 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.