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Robust adaptive observers for unknown linear exosystems
Author(s) -
Marino Riccardo,
Tomei Patrizio
Publication year - 2012
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.2346
Subject(s) - control theory (sociology) , eigenvalues and eigenvectors , adaptive control , scalar (mathematics) , mathematics , synchronization (alternating current) , linearization , signal (programming language) , linear system , decorrelation , estimator , computer science , nonlinear system , algorithm , control (management) , mathematical analysis , topology (electrical circuits) , physics , statistics , geometry , quantum mechanics , combinatorics , artificial intelligence , programming language
SUMMARY Given a measured scalar signal generated by an unknown linear exosystem with simple eigenvalues on the imaginary axis whose order is unknown, we address the problem of designing a robust adaptive exosystem of fixed order that is able to reproduce the measured signal within an error. The magnitude of such an error clearly depends on the unmodeled dynamics and vanishes if the order of the adaptive exosystem is greater than or equal to the order of the unknown exosystem. Adaptive exosystems are useful for prediction purposes, to generate successive time derivatives of the measured signal for control purposes (PID, model predictive control and feedback linearization) and in the design of regulators. The posed problem can also be interpreted as an adaptive synchronization problem in the presence of high frequency unmodeled dynamics for linear systems. It can also be viewed as the design of an estimator of m frequencies, amplitudes and phases by processing a signal constituted by the sum of r ≥ m sinusoidal terms. The posed problem will be solved by using the theory of robust adaptive observers and the key concept of persistency of excitation. Copyright © 2012 John Wiley & Sons, Ltd.