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Adaptive stabilization of LTI systems with distributed input delay
Author(s) -
BekiarisLiberis Nikolaos,
Jankovic Mrdjan,
Krstic Miroslav
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.2337
Subject(s) - backstepping , control theory (sociology) , constant (computer programming) , controller (irrigation) , key (lock) , actuator , computer science , state (computer science) , lyapunov function , adaptive control , control engineering , control (management) , engineering , nonlinear system , artificial intelligence , algorithm , quantum mechanics , agronomy , biology , programming language , physics , computer security
SUMMARY We solve stabilization problems of LTI systems with unknown parameters and distributed input delay. The key challenge is that the infinite‐dimensional input dynamics are distributed, which makes traditional infinite‐dimensional backstepping inapplicable. We resolve this challenge by employing backstepping–forwarding transformations of the finite‐dimensional state of the plant and of the infinite‐dimensional actuator state. These transformations enable us to design Lyapunov‐based update laws. We also design an adaptive controller for rejecting a constant disturbance in the input of the LTI plant, in the case where the parameters of the plant are known. Copyright © 2012 John Wiley & Sons, Ltd.