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Relative controllability of delay multi‐agent systems
Author(s) -
Si Yuanchao,
Fečkan Michal,
Wang JinRong,
O'Regan Donal
Publication year - 2021
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.5517
Subject(s) - controllability , kronecker product , controllability gramian , nonlinear system , mathematics , control theory (sociology) , rank condition , topology (electrical circuits) , fixed point theorem , linear system , rank (graph theory) , multi agent system , fixed point , controller (irrigation) , computer science , kronecker delta , control (management) , discrete mathematics , mathematical analysis , physics , quantum mechanics , combinatorics , artificial intelligence , agronomy , biology
Summary This article considers the controllability of delayed linear and nonlinear multi‐agent systems, respectively, with leader‐follower architecture and fixed communication topology. For the linear multi‐agent systems, a relative protocol is designed to realize the interactions among agents and explicit solutions of the controlled agreement system are constructed in two cases, respectively, involving two kinds of delayed exponential matrix functions and the properties of the Kronecker product. Further Gramian and rank criteria for relative controllability are established, respectively. For the nonlinear ones, the control problem is transformed into the existence of fixed points which is tackled via Krasnoselskii's fixed point theorem. Numerical examples of linear and nonlinear systems are given to verify the theoretical results.