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LPV modeling of nonlinear systems: A multi‐path feedback linearization approach
Author(s) -
Abbas Hossam S.,
Tóth Roland,
Petreczky Mihály,
Meskin Nader,
Mohammadpour Velni Javad,
Koelewijn Patrick J.W.
Publication year - 2021
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.5799
Subject(s) - affine transformation , linearization , representation (politics) , nonlinear system , observable , mathematics , canonical form , transformation (genetics) , control theory (sociology) , state space representation , path (computing) , scheduling (production processes) , computer science , algorithm , mathematical optimization , control (management) , pure mathematics , artificial intelligence , biochemistry , chemistry , physics , quantum mechanics , politics , political science , law , gene , programming language
This article introduces a systematic approach to synthesize linear parameter‐varying (LPV) representations of nonlinear (NL) systems which are described by input affine state‐space (SS) representations. The conversion approach results in LPV‐SS representations in the observable canonical form. Based on the relative degree concept, first the SS description of a given NL representation is transformed to a normal form. In the SISO case, all nonlinearities of the original system are embedded into one NL function, which is factorized, based on a proposed algorithm, to construct an LPV representation of the original NL system. The overall procedure yields an LPV model in which the scheduling variable depends on the inputs and outputs of the system and their derivatives, achieving a practically applicable transformation of the model in case of low order derivatives. In addition, if the states of the NL model can be measured or estimated, then a modified procedure is proposed to provide LPV models scheduled by these states. Examples are included to demonstrate both approaches.