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Research Papers

Consensus and Flocking With Connectivity Preservation of Uncertain Euler–Lagrange Multi-Agent Systems

[+] Author and Article Information
Yi Dong

Department of Automation,
Nanjing University of Science and Technology,
Nanjing 210000, China;
Department of Mechanical and
Automation Engineering,
The Chinese University of Hong Kong,
Hong Kong, China

Jie Huang

Department of Mechanical and
Automation Engineering,
The Chinese University of Hong Kong,
Hong Kong, China
e-mail: jhuang@mae.cuhk.edu.hk

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 18, 2016; final manuscript received February 28, 2018; published online April 30, 2018. Assoc. Editor: Manish Kumar.

J. Dyn. Sys., Meas., Control 140(9), 091011 (Apr 30, 2018) (8 pages) Paper No: DS-16-1449; doi: 10.1115/1.4039666 History: Received September 18, 2016; Revised February 28, 2018

The consensus problem for multiple Euler–Lagrange systems has been extensively studied under various assumptions on the connectivity of the communication graph. In practice, it is desirable to enable the control law the capability of maintaining the connectivity of the communication graph, thus achieving consensus without assuming the connectivity of the communication graph. We call such a problem as consensus with connectivity preservation. In this paper, we will study this problem for multiple uncertain Euler–Lagrange systems. By combining the adaptive control technique and potential function technique, we will show that such a problem is solvable under a set of standard assumptions. By employing different potential functions, our approach will also lead to the solution of such problems as rendezvous and flocking.

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Figures

Grahic Jump Location
Fig. 1

An example for potential function (3) with r = 1

Grahic Jump Location
Fig. 2

Distances dij=||qi−qj||, i,j=1,…,4, between initially connected agents

Grahic Jump Location
Fig. 3

Position of all agents qi, i=1,…,4

Grahic Jump Location
Fig. 4

Velocity of all agents q˙i, i=1,…,4

Grahic Jump Location
Fig. 5

The trajectory of θ̂i, i=1,…,4

Grahic Jump Location
Fig. 6

The distances dij=||qi−qj||, i,j=1,…,10, between initially connected agents

Grahic Jump Location
Fig. 7

The trajectory of q˙i when Λi=400I4 and Ki=400I2

Grahic Jump Location
Fig. 8

The trajectory of q˙i when Λi=40I4 and Ki=15I2

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