On the Controllability of Discrete-Time Leader-Follower Multiagent Systems with Two-Time-Scale and Heterogeneous Features

Mengqi Gu,Guo-Ping Jiang,Wenyu Zhang

doi:10.1155/2021/8893051

Abstract

This paper investigates the controllability of discrete-time leader-follower multiagent systems (MASs) with two-time-scale and heterogeneous features, motivated by the fact that many real systems are operating in discrete-time. In this study, singularly perturbed difference systems are used to model the two-time-scale heterogeneous discrete-time MASs. To avoid the ill-posedness problem caused by the singular perturbation parameter when using the classical control theory to study the model, the singular perturbation method was first applied to decompose the system into two subsystems with slow-time-scale and fast-time-scale feature. Then, from the perspective of algebra and graph theory, several easier-to-use controllability criteria for the related MASs are proposed. Finally, the effectiveness of the main results is verified by simulation.

Highlights

In recent years, with the wide application of multiagent systems (MASs) in aircraft formation, multirobot cooperative control, traffic vehicle control, network resource allocation, and other fields, scholars have become interested in the distributed cooperative control [1,2,3,4] of these systems
MASs are systems composed of some dynamic agents with the certain autonomous ability through information communication and interaction. e ultimate goal of studying them is reflected in the control that people can have, which makes the research on the controllability of MASs extremely important
In the 1960s, Kalman [5] introduced the concept of controllability of linear time-invariant (LTI) dynamic systems and pioneered the effective Kalman rank criterion for discriminating controllability of LTI dynamic systems. en, Tanner [6] extended the concept of controllability to MASs, aiming to understand more about the issue of single-integrator continuous-time in such systems

Summary

Introduction

With the wide application of MASs in aircraft formation, multirobot cooperative control, traffic vehicle control, network resource allocation, and other fields, scholars have become interested in the distributed cooperative control [1,2,3,4] of these systems. Su et al [26] first studied the controllability of discretetime first-order MASs with the two-time-scale feature and obtained necessary and/or sufficient controllability criteria based on the matrix theory. (2) A singularly perturbed difference system is used to model the discrete-time leader-follower MASs with heterogeneous and two-time-scale features, and the singular perturbation method is applied to decouple the model. (3) Several easier-to-use necessary and/or sufficient conditions for the controllability of discrete-time leader-follower MASs were obtained with heterogeneous and two-time-scale features. En, we define the controllability of the discrete-time leader-follower MASs with two-time-scale and heterogeneous features, and several necessary and/or sufficient conditions for controllability are stated.

Preliminaries and Problem Formulation

Main Results

Controllability Analysis