Frontiers of Information Technology & Electronic Engineering
>> 2016,
Volume 17,
Issue 2
doi:
10.1631/FITEE.1500490
Optimization of formation for multi-agent systems based on LQR
Affiliation(s): 1School of Automation, Hangzhou Dianzi University, Hangzhou 310018, China; 2Research School of Engineering, The Australian National University, Canberra ACT 0200, Australia; 3School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 611731, China; less
Received: 2015-12-30
Accepted: 2016-02-02
Available online: 2016-02-02
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Abstract
In this paper, three optimal linear algorithms are proposed for first-order linear from a 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 without initial physical couplings. The parameter matrix of the algorithm is the solution to an . It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected , 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 .
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