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Adaptive boundary stabilization for first‐order hyperbolic PDEs with unknown spatially varying parameter
Author(s) -
Xu Zaihua,
Liu Yungang
Publication year - 2015
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.3331
Subject(s) - backstepping , boundary (topology) , control theory (sociology) , projection (relational algebra) , mathematics , controller (irrigation) , hyperbolic partial differential equation , operator (biology) , adaptive control , computer science , partial differential equation , mathematical analysis , algorithm , control (management) , artificial intelligence , biochemistry , chemistry , repressor , transcription factor , gene , agronomy , biology
Summary The adaptive boundary stabilization is investigated for a class of systems described by first‐order hyperbolic PDEs with unknown spatially varying parameter. Towards the system unknowns, a dynamic compensation is first given by using infinite‐dimensional backstepping method, adaptive techniques, and projection operator. Then an adaptive controller is constructed by certainty equivalence principle, which can stabilize the original system in a certain sense. Moreover, the effectiveness of the proposed method is illustrated by a simulation example. Copyright © 2015 John Wiley & Sons, Ltd.