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Parametrization and geometric analysis of coordination controllers for multi-agent systems. (English) Zbl 1209.93012
The paper deals with the parametrization of the coordination controllers of multi-agent systems. A general expression of all the coordination controllers of the considered multi-agent systems is formulated. Following the results on the necessary and sufficient conditions for the formation stabilizing controllers [see Fax and Murray, Information flow and cooperative control of vehicle formation, IEEE Trans. Automat. Control 49, 1465–1476 (2004); G. Lafferriere, A. Williams, J. Caughman and J. J. P. Veerman, Syst. Control Lett. 54, No. 9, 899–910 (2005; Zbl 1129.93303)]) the authors show the geometric structures of coordination controllers with necessary and sufficient conditions for agent dynamics in general linear forms. It has been shown that the set of coordination controllers is diffeomorphic to the Cartesian product of the set of positive matrices and the set of skew symmetric matrices satisfying certain algebraic conditions. Based on parametrization, coordination problems are investigated for multi-agent systems with switching topologies.

93A14 Decentralized systems
93B25 Algebraic methods
35R35 Free boundary problems for PDEs
60G40 Stopping times; optimal stopping problems; gambling theory
62L15 Optimal stopping in statistics
49J40 Variational inequalities
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