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Adaptive controller design and disturbance attenuation for SISO linear systems with zero relative degree under noisy output measurements
Author(s) -
Zeng Sheng,
Pan Zigang,
Fernandez Emmanuel
Publication year - 2010
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.1132
Subject(s) - control theory (sociology) , robustness (evolution) , nonlinear system , adaptive control , robust control , mathematics , a priori and a posteriori , lyapunov function , linear system , controller (irrigation) , minimum phase , computer science , transfer function , engineering , control (management) , mathematical analysis , biochemistry , chemistry , physics , philosophy , epistemology , electrical engineering , quantum mechanics , artificial intelligence , biology , agronomy , gene
In this paper, we present robust adaptive controller design for SISO linear systems with zero relative degree under noisy output measurements. We formulate the robust adaptive control problem as a nonlinear H ∞ ‐optimal control problem under imperfect state measurements, and then solve it using game theory. By using the a priori knowledge of the parameter vector, we apply a soft projection algorithm, which guarantees the robustness property of the closed‐loop system without any persistency of excitation assumption of the reference signal. Owing to our formulation in state space, we allow the true system to be uncontrollable, as long as the uncontrollable part is stable in the sense of Lyapunov, and the uncontrollable modes on the jω‐axis are uncontrollable from the exogenous disturbance input. This assumption allows the adaptive controller to asymptotically cancel out, at the output, the effect of exogenous sinusoidal disturbance inputs with unknown magnitude, phase, and frequency. These strong robustness properties are illustrated by a numerical example. Copyright © 2009 John Wiley & Sons, Ltd.