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Research Papers

Distributed Optimal Consensus for Multi-Agent Systems Under Independent Position and Velocity Topology

[+] Author and Article Information
Chenyang Ding

School of Mathematics and Statistics,
Xidian University,
266 Xinglong Section of Xifeng Road,
Xi’an, Shaanxi 710126, China
e-mail: chosending2012@163.com

Junmin Li

School of Mathematics and Statistics,
Xidian University,
266 Xinglong Section of Xifeng Road,
Xi’an, Shaanxi 710126, China
e-mail: jmli@mail.xidian.edu.cn

Li Jinsha

School of Mathematics and Statistics,
Xidian University,
266 Xinglong Section of Xifeng Road,
Xi’an, Shaanxi 710126, China
e-mail: jinsha0321@163.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 4, 2016; final manuscript received March 6, 2017; published online June 28, 2017. Assoc. Editor: Manish Kumar.

J. Dyn. Sys., Meas., Control 139(10), 101012 (Jun 28, 2017) (7 pages) Paper No: DS-16-1338; doi: 10.1115/1.4036536 History: Received July 04, 2016; Revised March 06, 2017

In this paper, linear quadratic regulator (LQR) theory is applied to solve the inverse optimal consensus problem for a second-order linear multi-agent systems (MAS) under independent position and velocity topology. The optimal Laplacian matrices related to the topologies of position and velocity are derived by solving the algebraic Riccati equation (ARE). Theoretically, we obtain the optimal Laplacian matrices, which correspond to the directed strongly connected graphs, for the second-order multi-agent systems. Finally, two simulation examples are provided to verify the theoretical analysis of this paper.

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Figures

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Fig. 1

Position states under the optimal Laplacian matrices

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Fig. 2

Velocity states under the optimal Laplacian matrices

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Fig. 3

Control input of each agent under the optimal Laplacian matrix

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Fig. 4

Position states under the optimal Laplacian matrices

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Fig. 5

Velocity states under the optimal Laplacian matrices

Grahic Jump Location
Fig. 6

Control input of each agent under the optimal Laplacian matrix

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