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Decentralized minimal‐time planar formation control of multi‐agent system
Author(s) -
Ou Linlin,
Zou Chao,
Yu Xinyi
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3800
Subject(s) - polynomial , computer science , decentralised system , matrix (chemical analysis) , position (finance) , multi agent system , rank (graph theory) , path (computing) , mathematical optimization , mathematics , control theory (sociology) , topology (electrical circuits) , control (management) , mathematical analysis , combinatorics , artificial intelligence , materials science , finance , economics , composite material , programming language
Summary In this paper, the problems of decentralized minimal‐time planar formation control are investigated for both static and dynamic cases. For the static one, the discrete‐time dynamics of multi‐agent system in which each agent exchanges information according to a complex weighted network is studied. On the basis of a minimal polynomial, a decentralized minimal‐time static formation method is proposed to compute the final formation positions of the agents in the minimal number of steps without global coordinates. The proposed method allows an arbitrarily chosen agent in the network to compute its final formation position. For the dynamic one in a leader–follower framework, the path information of the agents satisfies linear regression equations that are determined by interaction topology and input signals. In order to obtain the coefficients of such linear regression equations, a Kronecker‐theorem‐based algorithm is presented. Similar to the results for the static case, any agent is allowed to use the minimum number of successive history state values to compute the future dynamic formation track. The minimal number of steps can be computed by checking the rank condition of the Hankel matrix constructed in terms of the path information. Meanwhile, the simulation examples are given to demonstrate the validity of the proposed minimal‐time planar formation control methods. The results in the paper combine the matrix polynomial analysis into the framework of formation control design and show how to predict the motion of the agents in a decentralized manner. Copyright © 2017 John Wiley & Sons, Ltd.