Premium
Extension of the tuning constant in the Huber's function for robust modeling of piezoelectric systems
Author(s) -
Corbier C.,
Carmona J.C.
Publication year - 2015
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2517
Subject(s) - estimator , hessian matrix , outlier , noise (video) , taylor series , errors in variables models , system identification , function (biology) , mathematics , covariance , computer science , parameterized complexity , control theory (sociology) , algorithm , mathematical optimization , artificial intelligence , statistics , data modeling , mathematical analysis , control (management) , database , evolutionary biology , image (mathematics) , biology
Summary This paper proposes a new modeling approach that is experimentally validated on piezoelectric systems in order to provide a black‐box pseudolinear model for complex systems control. Most of the time, one uses physical based approaches. However, sometimes complex phenomena occur in the system due to atypical changes of the process behavior, output noise or some hard nonlinearities. Therefore, we adopt identification methods to achieve the modeling task. The microdisplacements of the piezoelectric systems generate atypical data named outliers, leading to large estimated prediction errors. Since these errors disturb the classical normal probability density function, we choose here, as corrupted distribution model, the gross error model (GEM). In order to deal more efficiently with the outliers, we use the Huber's function, as mixed L 2 / L 1 norms in which the tuning threshold named scaling factor is extended. From this function, a cost function also named PREC as parameterized robust estimation criterion is established. The identification is performed by choosing an Output Error model structure. In order to express the asymptotic covariance matrix of the robust estimator, we present a L finite Taylor's expansion to linearize the gradient and the hessian of the PREC. Experimental results are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.