  This article aims to improve the performance of networked multi-agent
systems, which are common representations of cyber-physical systems. The rate
of convergence to consensus of multi-agent networks is critical to ensure
cohesive, rapid response to external stimuli. The challenge is that increasing
the rate of convergence can require changes in the network connectivity, which
might not be always feasible. Note that current consensus-seeking control laws
can be considered as a gradient-based search over the graph's Laplacian
potential. The main contribution of this article is to improve the convergence
to consensus, by using an accelerated gradient-based search approach.
Additionally, this work shows that the accelerated-consensus approach can be
implemented in a distributed manner, where each agent applies a delayed self
reinforcement, without the need for additional network information or changes
to the network connectivity. Simulation results of an example networked system
are presented in this work to show that the proposed accelerated-consensus
approach with DSR can substantially improve synchronization during the
transition by about ten times, in addition to decreasing the transition time by
about half, when compared to the case without the DSR approach. This is shown
to improve formation control during transitions in networked multi-agent
systems.
