Iterative Learning Consensus of Fractional-Order Multi-Agent Systems Subject to Iteration-Varying Initial State Shifts

Liming Wang

doi:10.1109/access.2019.2952673

Abstract

This paper investigates the robust consensus tracking problem of fractional-order multiagent systems (FOMASs) subject to the iteration-varying initial state shifts. For the FOMASs including one leader agent and multiple follower agents, the PD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> -type ILC protocol with the rectifying action is proposed. By improving the existing average operator and choosing the suitable variables, the leaderfollowing FOMASs under the proposed protocol are rewritten as a two-dimensional (2D) dynamical model. Based on the 2D analysis approach, the sufficient conditions are presented for the consensus of FOMASs. It is shown that due to the improved average operator, the derived sufficient conditions are more relaxed. With the increase of iteration step, the output of each follower agent will converge, and as the iteration step goes to infinity, and the limit output of each follower agent can be formulated in terms of the output of leader agent, the mean values of the initial output tracking errors, the learning gain matrices, the fractional order and the structure of communication graph. Finally, two numerical simulation examples are presented to demonstrate the effectiveness of the proposed method.

Highlights

With the research of the integer-order multi-agent systems (IOMASs) [1]–[5] and the development of the fractional calculus [6], numerous researchers turn their attention to the fractional-order multi-agent systems (FOMASs)
Inspired by the existing iterative learning control (ILC) consensus research of FOMASs and the obvious differences between the existing consensus convergence conditions [31]–[33], we investigate the robust consensus tracking problem of leader-following FOMASs subject to the iteration-varying initial state shifts
By improving the existing average operator, the PDα-type ILC consensus protocol with the rectifying action is designed and the leader-following FOMASs are rewritten as a two-dimensional (2D) model, thereby the more relaxed consensus convergence conditions can be derived based on the 2D analysis approach

Summary

INTRODUCTION

With the research of the integer-order multi-agent systems (IOMASs) [1]–[5] and the development of the fractional calculus [6], numerous researchers turn their attention to the fractional-order multi-agent systems (FOMASs). Inspired by the existing ILC consensus research of FOMASs and the obvious differences between the existing consensus convergence conditions [31]–[33], we investigate the robust consensus tracking problem of leader-following FOMASs subject to the iteration-varying initial state shifts. By improving the existing average operator, the PDα-type ILC consensus protocol with the rectifying action is designed and the leader-following FOMASs are rewritten as a two-dimensional (2D) model, thereby the more relaxed consensus convergence conditions can be derived based on the 2D analysis approach. The existing ILC literatures have investigated the consensus of IOMASs subject to the strict identical initial states/outputs [18]–[22], the fixed initial state/output shifts [23], [24] and the initial alignment conditions [25]–[30], while the iteration-varying initial states/output shifts haven’t been considered in the MASs framework. The conclusions are drawn from the present studies in the last section

BACKGROUND

SOME DEFINITIONS AND LEMMAS

CONCLUSION