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Optimization of formation for multi-agent systems based on LQR

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Abstract

In this paper, three optimal linear formation control algorithms are proposed for first-order linear multiagent 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.

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Authors and Affiliations

  1. School of Automation, Hangzhou Dianzi University, Hangzhou, 310018, China

    Chang-bin Yu & Yin-qiu Wang

  2. Research School of Engineering, The Australian National University, Canberra, ACT, 0200, Australia

    Chang-bin Yu

  3. School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Jin-liang Shao

Authors
  1. Chang-bin Yu
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  2. Yin-qiu Wang
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  3. Jin-liang Shao
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Corresponding author

Correspondence to Yin-qiu Wang.

Additional information

Project supported by the National Natural Science Foundation of China (No. 61375072) (50%) and the Natural Science Foundation of Zhejiang Province, China (No. LQ16F030005) (50%)

ORCID: Yin-qiu WANG, http://orcid.org/0000-0002-1410-9619

Dr. Chang-bin YU, first author of this invited paper, received his Bachelor degree in Computer Engineering from Nanyang Technological Unviersity, Singapore, in 2004, and PhD degree in Engineering from the Australian National University, Australia, in 2008. Since then, he has been an academic staff with the Australian National University and subsequently held various appointments with Hangzhou Dianzi University (China), National ICT Australia (Australia), etc. His current research interests include control of autonomous formations, multiagent systems, mobile sensor networks, human-robot interation, and graph theory. He is Associate Editor of International Journal of Robust and Nonlinear Control.

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Yu, Cb., Wang, Yq. & Shao, Jl. Optimization of formation for multi-agent systems based on LQR. Frontiers Inf Technol Electronic Eng 17, 96–109 (2016). https://doi.org/10.1631/FITEE.1500490

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  • DOI: https://doi.org/10.1631/FITEE.1500490

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