Time-Varying and Nonlinearly Scaled Consensus of Multiagent Systems: A Generic Attracting Law Approach

TL;DR

This paper introduces a generic attracting law for multiagent systems that achieves finite and fixed-time consensus using time-varying and nonlinear scales, with theoretical analysis and numerical validation.

Contribution

It proposes a novel generic attracting law and distributed protocols for finite/fixed-time consensus in multiagent systems with complex scaling strategies.

Findings

Finite/fixed-time consensus is achievable with the proposed methods.

Derived bounds on convergence times depend on initial states.

Numerical examples confirm the effectiveness of the protocols.

Abstract

This paper presents the design and analysis of the finite/fixed-time scaled consensus for multiagent systems. A study on a generic attracting law, the certain classes of nonlinear systems that admit attractors with finite/fixed-time convergence, is at first given for the consensus purpose. The estimates for the lower and upper bounds on the settling time functions are provided through the two-phase analysis. The given estimates are initial state dependent, but the durations are finite, without regarding the values that the initial states take. According to the generic attracting law, distributed protocols are proposed for multiagent systems with undirected and detail-balanced directed graphs, respectively, where the scaled strategies, including time-varying and nonlinear scales, are adopted. It is shown that the finite/fixed-time consensus for the multiagent system undertaken can still be achieved, even though both time-varying and nonlinear scales are taken among agents. Numerical simulation of two illustrative examples are given to verify effectiveness of the proposed finite-duration consensus protocols.