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Adaptive output‐feedback stabilisation of an uncertain second‐order linear systems
Author(s) -
AguilarIbanez Carlos,
Acosta José Ángel,
MartinezGarcia Juan C.,
GarcíaCanseco Eloísa
Publication year - 2017
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2735
Subject(s) - control theory (sociology) , backstepping , nonlinear system , adaptive control , observer (physics) , stability (learning theory) , computer science , sign (mathematics) , mathematics , control (management) , control engineering , mathematical optimization , engineering , artificial intelligence , mathematical analysis , physics , quantum mechanics , machine learning
Summary The adaptive stabilisation of uncertain second‐order linear systems is addressed, under a lack of information from both states and parameters. The only standard assumptions are no zeros and the sign of the high frequency gain known. To the best of the authors' knowledge, there has been only an explicit solution proposed in the literature so far with proven stability. Despite the simplicity of the system, it does not fit in any of the standard nonlinear control methodologies available. Thus, this work is a complementary contribution providing a mixed control design strategy based on a reduced‐order observer, adaptive Immersion & Invariance and Backstepping approaches. Hence, this solution depicts a transversal outlook of those nonlinear control strategies and provides a breakthrough for the generalisation of this non‐trivial control problem. Numerical simulations are reported to assess the effectiveness of the adaptive strategy. Copyright © 2016 John Wiley & Sons, Ltd.