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CLC number: TP273

On-line Access: 2016-02-02

Received: 2015-12-30

Revision Accepted: 2016-01-20

Crosschecked: 2016-01-22

Cited: 1

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Citations:  Bibtex RefMan EndNote GB/T7714


Yin-qiu Wang


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Frontiers of Information Technology & Electronic Engineering  2016 Vol.17 No.2 P.96-109


Optimization of formation for multi-agent systems based on LQR

Author(s):  Chang-bin Yu, Yin-qiu Wang, Jin-liang Shao

Affiliation(s):  1School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China; more

Corresponding email(s):   brad.yu@anu.edu.au, wh6508@gmail.com, jinliangshao@126.com

Key Words:  Linear quadratic regulator (LQR), Formation control, Algebraic Riccati equation (ARE), Optimal control, Multi-agent systems

Chang-bin Yu, Yin-qiu Wang, Jin-liang Shao. Optimization of formation for multi-agent systems based on LQR[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(2): 96-109.

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A1 - Chang-bin Yu
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A1 - Jin-liang Shao
J0 - Frontiers of Information Technology & Electronic Engineering
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DOI - 10.1631/FITEE.1500490

In this paper, three optimal linear formation control algorithms are proposed for first-order linear multi-agent systems from a linear quadratic regulator (LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost, because both the collective object (such as formation or consensus) and the individual goal of each agent are very important for the overall system. First, we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings. The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation (ARE). It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected multi-agent systems, the optimal formation algorithm is presented, and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown. Finally, if the communication topology between agents is fixed, the local feedback gain is obtained from the solution to a quadratic equation with one unknown. The equation is derived from the derivative of the cost function with respect to the local feedback gain. Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.

The authors of this paper provide three algorithms for optimal linear formation control of multi-agent systems. The agents are considered to have single integrator dynamics. In this connection they used LQR method to minimize collective objective of all agents and the individual objective of each agent. Three cases of independent agents, physically bounded agents, and a network of agents with fixed topology are considered. The paper is technically correct and the mathematical derivations are accurate. The results are a bit interesting.




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