Multiple Intentional Delays Can Facilitate Fast Consensus and Noise Reduction in a Multiagent System.

We investigate the use of a derivative-free control scheme called the multiple-delay proportional-retarded (PR) protocol to achieve fast consensus in a large-scale multiagent system. The delays are intentionally introduced in the PR with the purpose of creating derivative-like controllers that rely only on position measurements, thus mitigating undesirable noise effects. The main result places the spectral abscissa of the consensus dynamics at a desired locus and also achieves a user-defined spectral "separation," both of which directly influence convergence to consensus. Design rules and limitations arising from analytical derivations to achieve these results are laid out. Case studies are provided to demonstrate the concepts.