On predefined-time consensus protocols for dynamic networks

TL;DR

This paper introduces new fixed-time consensus protocols for dynamic networks that guarantee convergence within a user-defined time, independent of initial conditions, and improve upon existing methods by offering greater flexibility and efficiency.

Contribution

The paper develops novel classes of predefined-time consensus protocols that extend current fixed-time methods, allowing for customizable convergence bounds and reduced computational complexity.

Findings

Protocols ensure convergence within a predefined time bound.

One protocol achieves average consensus even in switching networks.

Simulations validate the effectiveness of the proposed methods.

Abstract

This paper presents new classes of consensus protocols with fixed-time convergence, which enable the definition of an upper bound for consensus state as a parameter of the consensus protocol, ensuring its independence from the initial condition of the nodes. We demonstrate that our methodology subsumes current classes of fixed-time consensus protocols that are based on homogeneous in the bi-limit vector fields. Moreover, the proposed framework enables for the development of independent consensus protocols that are not needed to be homogeneous in the bi-limit. This proposal offers extra degrees of freedom to implement consensus algorithms with enhanced convergence features, such as reducing the gap between the real convergence moment and the upper bound chosen by the user. We present two classes of fixed-time consensus protocols for dynamic networks, consisting of nodes with first-order dynamics, and provide sufficient conditions to set the upper bound for convergence a priori as a consensus protocol parameter. The first protocol converges to the average value of the initial condition of the nodes, even when switching among dynamic networks. Unlike the first protocol, which requires, at each instant, an evaluation of the non-linear predefined time-consensus function, hereinafter introduced, per neighbor, the second protocol requires only a single evaluation and ensures a predefined time-consensus for static topologies and fixed-time convergence for dynamic networks. Predefined-time convergence is proved using Lyapunov analysis, and simulations are carried out to illustrate the performance of the suggested techniques. The exposed results have been applied to the design of predefined time-convergence formation control protocols to exemplify their main features.