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Adaptive tracking of stochastic nonlinear systems with Prandtl–Ishlinskii hysteresis
Author(s) -
Liu Wei,
Ji Haibo,
Ma Yike
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.1781
Subject(s) - backstepping , control theory (sociology) , nonlinear system , tracking error , hysteresis , residual , covariance , tracking (education) , mathematics , quartic function , lyapunov function , computer science , adaptive control , control (management) , algorithm , physics , artificial intelligence , psychology , pedagogy , statistics , quantum mechanics , pure mathematics
SUMMARY This paper deals with adaptive tracking problems for a class of stochastic nonlinear systems with unknown hysteresis nonlinearities. The system considered is in a strict‐feedback form driven by unknown Prandtl–Ishlinskii hysteresis and Wiener noises of unknown covariance. By employing backstepping design techniques and stochastic Lyapunov design method, parameter adaptive laws and control laws are obtained, which ensure that the tracking error can converge to a small residual set around the origin in the sense of mean quartic value. Copyright © 2011 John Wiley & Sons, Ltd.