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Approximate gradients, convergence and positive realness in recursive identification of a class of non‐linear systems
Author(s) -
Wigren Torbjörn
Publication year - 1995
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.4480090403
Subject(s) - control theory (sociology) , linearity , cascade , mathematics , quantization (signal processing) , convergence (economics) , transfer function , system identification , nonlinear system , computer science , algorithm , engineering , physics , control (management) , electrical engineering , quantum mechanics , database , artificial intelligence , chemical engineering , economics , measure (data warehouse) , economic growth
Recursive identification algorithms based on the Wiener model are presented in this paper. They estimate the parameters of a SISO linear dynamic block in cascade with a known static output non‐linearity. Inversion of the non‐linear function is avoided and approximations of gradients are utilized. This allows an exact treatment of output measurement saturation and of situations where output measurements are obtained from sensors with relay‐type characteristics, such as EGO sensors in emission control systems for cars. Exact compensation for coarse quantization of output measurements can also be obtained by the algorithms. Stochastic averaging techniques using associated differential equations prove that local and global convergence of the schemes are tied to positive realness and sector conditions on the non‐linearity. Conditions for local convergence to the correct parameters are established for the case where the output non‐linearity is an arbitrary quantizer.