In this technical note, we first clarify a technical issue in the convergence proof of a free-will arbitrary time (FwAT) consensus law proposed recently in Pal et al. IEEE Trans. Cybern. (2020)[1], making the results questionable. We then propose free-will arbitrary time consensus protocols for multi-agent systems with first- and second-order dynamics, respectively, and with (possibly switching) connected interaction graphs. Under the proposed consensus laws, we show that an average consensus is achieved in a free-will arbitrary prespecified time. Further, the proposed consensus laws are distributed in the sense that information is only communicated locally between neighboring agents; unlike the average consensus in [1] that uses a deformed Laplacian.
@article{arxiv.2108.07150,
title = {Free-Will Arbitrary Time Consensus Protocols with Diffusive Coupling},
author = {Quoc Van Tran and Minh Hoang Trinh and Nam Hoai Nguyen and Hyo-Sung Ahn},
journal= {arXiv preprint arXiv:2108.07150},
year = {2021}
}