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Adaptive discrete neural observer design for nonlinear systems with unknown time‐delay
Author(s) -
Na Jing,
Herrmann Guido,
Ren Xuemei,
Barber Phil
Publication year - 2011
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.1612
Subject(s) - control theory (sociology) , nonlinear system , lipschitz continuity , observer (physics) , mathematics , lemma (botany) , artificial neural network , lyapunov function , converse , norm (philosophy) , discrete time and continuous time , computer science , control (management) , mathematical analysis , artificial intelligence , statistics , physics , quantum mechanics , ecology , geometry , poaceae , political science , law , biology
This paper focuses on the adaptive observer design for nonlinear discrete‐time MIMO systems with unknown time‐delay and nonlinear dynamics. The delayed states involved in the system are arguments of a nonlinear function and only the estimated delay is utilized. By constructing an appropriate Lyapunov–Krasovskii function, the delay estimation error is considered in the observer parameter design. The proposed method is then extended to the system with a nonlinear output measurement equation and the delayed dynamics. With the help of a high‐order neural network (HONN), the requirement for a precise system model, the linear‐in‐the‐parameters (LIP) assumption of the delayed states, the Lipschitz or norm‐boundedness assumption of unknown nonlinearities are removed. A novel converse Lyapunov technical lemma is also developed and used to prove the uniform ultimate boundedness of the proposed observer. The effectiveness of the proposed results is verified by simulations. Copyright © 2010 John Wiley & Sons, Ltd.