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Robust output regulation and the preservation of polynomial closed‐loop stability
Author(s) -
Paun Lassi,
Pohjolainen S.
Publication year - 2014
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.3064
Subject(s) - control theory (sociology) , robustness (evolution) , closed loop , polynomial , robust control , stability (learning theory) , exponential stability , computer science , mathematics , control system , control engineering , control (management) , engineering , nonlinear system , artificial intelligence , mathematical analysis , biochemistry , chemistry , physics , electrical engineering , machine learning , quantum mechanics , gene
SUMMARY In this paper, we study the robust output regulation problem for distributed parameter systems with infinite‐dimensional exosystems. The main purpose of this paper is to demonstrate the several advantages of using a controller that achieves polynomial closed‐loop stability, instead of a one stabilizing the closed‐loop system strongly. In particular, the most serious unresolved issue related to strongly stabilizing controllers is that they do not possess any known robustness properties. In this paper, we apply recent results on the robustness of polynomial stability of semigroups to show that, on the other hand, many controllers achieving polynomial closed‐loop stability are robust with respect to large and easily identifiable classes of perturbations to the parameters of the plant. We construct an observer based feedback controller that stabilizes the closed‐loop system polynomially and solves the robust output regulation problem. Subsequently, we derive concrete conditions for finite rank perturbations of the plant's parameters to preserve the closed‐loop stability and the output regulation property. The theoretical results are illustrated with an example where we consider the problem of robust output tracking for a one‐dimensional heat equation.Copyright © 2013 John Wiley & Sons, Ltd.