Free-Will Arbitrary Time Consensus Protocols with Diffusive Coupling

TL;DR

This paper corrects a previous convergence proof and introduces new distributed free-will arbitrary time consensus protocols for multi-agent systems, ensuring average consensus within a user-prescribed time frame.

Contribution

It provides a corrected theoretical foundation and novel consensus protocols that work with switching graphs and arbitrary time, enhancing control over multi-agent coordination.

Findings

Achieves average consensus in a user-prescribed time

Protocols work with switching interaction graphs

Ensures distributed implementation with local communication

Abstract

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.