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Nonlinear adaptive learning control for unknown time‐varying parameters and unknown time‐varying delays
Author(s) -
Chen Weisheng,
Zhang Zhengqiang
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.403
Subject(s) - control theory (sociology) , nonlinear system , convergence (economics) , tracking error , adaptive control , tracking (education) , function (biology) , computer science , lyapunov function , control (management) , mathematics , artificial intelligence , psychology , pedagogy , physics , quantum mechanics , evolutionary biology , economics , biology , economic growth
A new adaptive learning control approach is proposed for a class of first‐order nonlinear systems with two unknown time‐varying parameters and an unknown time‐varying delay. By reconstructing the system equation, all unknown time‐varying terms, including the time‐varying delay, are combined into an unknown periodic time‐varying vector, which is estimated by a periodic adaptive mechanism. By constructing a Lyapunov–Krasovskii‐like composite energy function (CEF), we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to two classes of high‐order nonlinear systems with mixed parameters. Three simulation examples are provided to illustrate the effectiveness of the control algorithms proposed in this paper.Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society