Energy-Limited Time-Varying Formation Control for Second-Order Multiagent Systems

Le Wang,Wanzhen Quan,Xiaogang Yang,Yulong Zhao,Ning Cai

doi:10.1155/2020/8867820

Abstract

The energy-limited time-varying formation (ETVF) control problem of second-order multiagent systems (MAS) is addressed for both leaderless and leader-following communication topologies in this paper. Different from the previous results, the joint consideration of energy limitation and formation design is more challenging and practical. First, an ETVF control protocol is presented, and the total energy supply is pregiven and limited, which is more common in practical applications. Then, by an orthogonal transformation, the formation control problem is converted into the consensus stabilization problem for second-order leaderless MAS, where sufficient conditions for the ETVF are derived by joint design of control gains and the total energy. At the same time, the explicit formula that forms the formation center function is obtained to depict the macroscopic movement of the multiagent system as a whole. Moreover, the proposed method is also extended to the leader-following communication structure. Finally, two examples are given to verify the effectiveness of our theoretical results.

Highlights

The topic of cooperative control of multiagent systems (MAS) has been paid increasing attention due to its wide application in many fields, such as sensor network synchronization [1,2,3], formation control [4,5,6,7], flocking [8, 9], and so on
Many scholars found that the above cooperative behavior among agents is based on the swarm consensus [10,11,12,13,14,15,16,17], and all agents could perform tasks that cannot be achieved by a single one as a formation structure. e formation control, as a fundamental and key issue of cooperative control, refers to a team of interacting agents to perform complex tasks together in a certain geometric structure, which is applied to many fields, such as networking system of satellite clusters, movements of mobile robotics [18, 19], cooperative attack of multiple missiles [20], and unmanned aerial vehicle formations [21, 22]
It is well known that the formation can be divided into the time-invariant and time-varying formation according to variation of formation structures

Summary

Introduction

The topic of cooperative control of MAS has been paid increasing attention due to its wide application in many fields, such as sensor network synchronization [1,2,3], formation control [4,5,6,7], flocking [8, 9], and so on. Motivated by the aforementioned facts and challenges, the problems of time-varying formation for MAS with limited energy in leaderless and leader-following cases are studied in this paper, respectively. The problem of limited energy supply is taken into consideration based on practical engineering, where a joint design strategy combining time-varying formation control and energy constraints is investigated. In this case, the desired formation structure must be formed and the practical energy consumption of the time-varying formation is less than the given energy, where the practical energy is a performance index function composed of the quadratic form of the control protocol.

Preliminaries

Numerical Simulation