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Performance‐oriented quasi‐LPV modeling of nonlinear systems
Author(s) -
Robles Ruben,
Sala Antonio,
Bernal Miguel
Publication year - 2018
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.4444
Subject(s) - nonlinear system , embedding , control theory (sociology) , controller (irrigation) , convex hull , computer science , mathematical optimization , regular polygon , set (abstract data type) , projection (relational algebra) , linear system , mathematics , control (management) , algorithm , artificial intelligence , mathematical analysis , physics , geometry , quantum mechanics , agronomy , biology , programming language
Summary Polytopic quasi–linear parameter‐varying (quasi‐LPV) models of nonlinear processes allow the usage linear matrix inequalities (LMIs) to guarantee some performance goal on them (in most cases, locally, over a so‐called modeling region). In order to get a finite number of LMIs, nonlinearities are embedded on the convex hull of a finite set of linear models. However, for a given system, the quasi‐LPV representations are not unique, yielding different performance bounds depending on the model choice. To avoid such drawback, earlier literature on the topic used annihilator‐based approaches, which require gridding on the modeling region, and nonconvex BMI conditions for controller synthesis; optimal performance bounds are obtained, but with a huge computational burden. This paper proposes building a model by minimizing the projection of the nonlinearities onto directions, which are deleterious for performance. For a small modeling region, these directions are obtained from LMIs with the linearized model. Additionally, these directions will guide the selection of the polytopic embedding's vertices. The procedure allows gridding‐free LMI controller synthesis, as in standard LPV setups, with a very reduced performance loss with respect to the aforementioned BMI+gridding approaches, at a fraction of the computational cost.