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Stabilization of a spatially non‐causal reaction–diffusion equation by boundary control
Author(s) -
Guo C.,
Xie C.,
Zhou C.
Publication year - 2012
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.2864
Subject(s) - backstepping , transformation (genetics) , boundary (topology) , reaction–diffusion system , stability (learning theory) , heat equation , mathematics , diffusion , control theory (sociology) , space (punctuation) , inverse , series (stratigraphy) , diffusion equation , mathematical analysis , control (management) , computer science , physics , adaptive control , chemistry , engineering , thermodynamics , geometry , operations management , artificial intelligence , metric (unit) , operating system , biochemistry , machine learning , gene , biology , paleontology
SUMMARY Stabilization of a reaction–diffusion equation, in which the heat source depends on the temperature of the whole space, is considered by using boundary control. A new backstepping transformation is introduced, in which there are two kernels. Through a series of mathematical tricks, the exact solutions of kernels are obtained, and a control law is obtained specifically. The inverse transformation is derived, and stability of the closed loop system established. Simulation results show that the closed loop system is stable. Copyright © 2012 John Wiley & Sons, Ltd.