Sliding mode control for N‐coupled reaction‐diffusion PDEs with boundary input disturbances

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...

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Bibliographic Details
Published inInternational journal of robust and nonlinear control Vol. 29; no. 5; pp. 1437 - 1461
Main Authors Gu, Jian‐Jun, Wang, Jun‐Min
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 25.03.2019
Subjects
backstepping
Coupled modes
disturbance rejection
Disturbances
N‐coupled reaction‐diffusion PDEs
Parabolic differential equations
Riesz basis
Sliding mode control
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Summary: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.
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ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.4448