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A theoretical framework for gain scheduling
Author(s) -
Fromion Vincent,
Scorletti Gérard
Publication year - 2003
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.748
Subject(s) - gain scheduling , mathematical optimization , scheduling (production processes) , nonlinear system , minification , computer science , norm (philosophy) , control theory (sociology) , mathematics , control (management) , artificial intelligence , political science , law , physics , quantum mechanics
The weighted incremental norm approach was originally introduced as a natural framework for extending well‐known H ∞ linear control concepts into the nonlinear context. In this paper, we investigate the numerous links between this new approach and the classical gain‐scheduling technique. Although based on heuristic rules, gain‐scheduled control is probably the most widespread nonlinear technique. In this paper, we point out that the control objectives of the gain‐scheduled controller design can be expressed as the weighted incremental norm minimization of a nonlinear operator. The result interest is twofold: it first provides a rigorous mathematical formulation of the gain‐scheduling problem. Furthermore, existing gain‐scheduling techniques can be interpreted as approximate solutions to the weighted incremental norm minimization of a nonlinear operator. Copyright © 2003 John Wiley & Sons, Ltd.