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Design of a class of nonlinear consensus protocols for multi‐agent systems
Author(s) -
Xu Yaojin,
Tian YuPing
Publication year - 2012
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.2838
Subject(s) - algebraic graph theory , consensus , algebraic connectivity , nonlinear system , multi agent system , computer science , uniform consensus , bounded function , laplacian matrix , directed graph , spanning tree , protocol (science) , convergence (economics) , graph , class (philosophy) , topology (electrical circuits) , integrator , theoretical computer science , mathematics , algorithm , discrete mathematics , artificial intelligence , computer network , alternative medicine , economic growth , mathematical analysis , bandwidth (computing) , pathology , quantum mechanics , medicine , physics , combinatorics , economics
SUMMARY This paper investigates the consensus problem for multi‐agent systems and presents a class of nonlinear consensus protocols. First, we reveal some structure property of the corresponding Laplacian matrix by decomposing the interaction graph into strongly connected components. Then, by means of the input‐to‐state stability and algebraic graph theory, we propose a framework to prove consensus for multi‐agent systems with nonlinear protocols. In particular, we prove that consensus can be always reached in systems of single‐integrator agents with a directed communication topology containing a spanning tree, provided the nonlinear protocol is an odd and increasing function. The nonlinear consensus protocols proposed in this paper include the classical linear consensus protocol as a special case, and may have a wide range of applications, including consensus with faster convergence rates and with bounded control inputs. Copyright © 2012 John Wiley & Sons, Ltd.