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Sliding mode control for N ‐coupled reaction‐diffusion PDEs with boundary input disturbances
Author(s) -
Gu JianJun,
Wang JunMin
Publication year - 2018
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.4448
Subject(s) - backstepping , control theory (sociology) , boundary (topology) , sliding mode control , convergence (economics) , mathematics , trajectory , surface (topology) , mode (computer interface) , diffusion , mathematical analysis , computer science , control (management) , adaptive control , physics , nonlinear system , geometry , astronomy , economics , economic growth , thermodynamics , quantum mechanics , artificial intelligence , operating system
Summary This paper develops the sliding mode control (SMC) design for N ‐coupled reaction‐diffusion parabolic PDEs with boundary input disturbances. In order to reject the disturbances, the backstepping‐based boundary SMC law is constructed to steer the system trajectory to a suitable sliding surface and then maintain sliding motion on the surface thereafter, resulting in the exponential convergence to the zero equilibrium state. The well‐posedness of the closed‐loop system is established based on a detailed spectral analysis and Riesz basis generation. Finally, a simulation example is provided to illustrate the effectiveness of the SMC design.