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Decomposition of the min–max multi‐model problem via integral sliding mode
Author(s) -
Fridman L.,
Poznyak A.,
Bejarano F.
Publication year - 2005
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.1009
Subject(s) - robustification , integral sliding mode , dimension (graph theory) , control theory (sociology) , invariant (physics) , mode (computer interface) , process (computing) , mathematical optimization , mathematics , control (management) , computer science , sliding mode control , physics , nonlinear system , artificial intelligence , quantum mechanics , mathematical physics , operating system , pure mathematics
The concept of the integral sliding mode (ISM) is revised and applied for robustification of a linear time invariant min–max multi‐model problem with uncertainties. Modified version of ISM ensures the insensitivity of the designed min–max control law with respect to matched uncertainty, starting from the beginning of the process, and guarantees that the unmatched part of uncertainties is minimized and not amplified . Proposed ISM dynamics allows to reduce the dimension [ Nn ] of the min–max control design problem to the space of unmatched uncertainties only of [ Nn −( N −1) m ] size. A numerical example illustrates that the suggested modification of the ISM dynamics does not change the min–max control as well as the value of the corresponding performance index. Copyright © 2005 John Wiley & Sons, Ltd.