Fractional-Order Iterative Learning Control with Initial State Learning for a Class of Multiagent Systems

Xungen Li,Mian Pan,Qi Ma,Shuaishuai Lv,Wenyu Cai,Oh-Min Kwon

doi:10.1155/2020/9130875

Abstract

To solve the consensus problem of fractional-order multiagent systems with nonzero initial states, both open- and closed-loop PDα-type fractional-order iterative learning control are presented. Considering the nonzero states, an initial state learning mechanism is designed. The finite time convergences of the proposed methods are discussed in detail and strictly proved by using Lebesgue-p norm theory and fractional-order calculus. The convergence conditions of the proposed algorithms are presented. Finally, some simulations are applied to verify the effectiveness of the proposed methods.

Highlights

Fractional-order multiagent systems (FOMASs) is composed of multiple agents, which can coordinate with each other to perceive the external environment, and apply fractional-order calculus principle
Fault tolerance, flexibility, scalability, and collaboration capabilities of the FOMASs, it can be applied to the intelligent environment perception and intelligent operation, such as air formation control, traffic vehicle control, data convergence, sensor networks, and so on [1,2,3,4]
In [10, 11], the adaptive control and the sampling data control were designed to solve the consensus problem of nonlinear and linear FOMASs with and without leader-following structure, and some sufficient and necessary conditions related to fractional order, coupling gain, and Laplacian matrix spectrum were obtained to ensure that the system can achieve consensus

Summary

Introduction

Fractional-order multiagent systems (FOMASs) is composed of multiple agents, which can coordinate with each other to perceive the external environment, and apply fractional-order calculus principle. Most of the research just consider the asymptotic convergence problem of FOMASs, which means the tracking errors of the fractional-order agents gradually converge to zero as time increases. Fractional-order iterative learning control (FOILC) methods for repetitive running systems can achieve complete tracking problems in finite time [15,16]. For the linear time-varying integer-order system, Luo et al proposed a FOILC framework with initial state learning and presented sufficient and necessary conditions for open-loop and closed-loop Dα-type FOILC. For linear time-varying FOMASs with fixing the initial states over the directed graph, we design several fractional iterative learning controllers with the initial states learning algorithms.

Preliminaries

Fractional Calculus

Problem Description

Simulation

Conclusion