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Formation‐containment analysis and design for high‐order linear time‐invariant swarm systems
Author(s) -
Dong Xiwang,
Shi Zongying,
Lu Geng,
Zhong Yisheng
Publication year - 2014
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.3274
Subject(s) - containment (computer programming) , swarm behaviour , convex hull , mathematical optimization , computer science , invariant (physics) , control theory (sociology) , mathematics , control (management) , regular polygon , programming language , geometry , artificial intelligence , mathematical physics
Summary Formation‐containment analysis and design problems for high‐order linear time‐invariant swarm systems with directed interaction topologies are dealt with respectively. Firstly, protocols are presented for leaders and followers respectively to drive the states of leaders to realize the predefined time‐varying formation and propel the states of followers to converge to the convex hull formed by the states of leaders. Secondly, formation‐containment problems of swarm systems are transformed into asymptotic stability problems, and an explicit expression of the formation reference function is derived. Sufficient conditions for swarm systems to achieve formation containment are proposed. Furthermore, necessary and sufficient conditions for swarm systems to achieve containment and time‐varying formation are presented respectively as special cases. An approach to determine the gain matrices in the protocols is given. It is shown that containment problems, formation control problems, consensus problems and consensus tracking problems can all be treated as special cases of formation‐containment problems. Finally, numerical simulations are provided to demonstrate theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.