Prescribed-time stabilisation for uncertain reaction-diffusion equations with Neumann boundary control

We study the Neumann boundary feedback stabilisation for reaction-diffusion equations with matched boundary uncertainties (including internal uncertainty and external disturbance) within a prescribed time, where the convergence time is independent of initial conditions and can be prescribed a priori...

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Bibliographic Details
Published inInternational journal of control Vol. 96; no. 9; pp. 2374 - 2383
Main Authors Wei, Chengzhou, Li, Junmin, He, Chao
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.09.2023
Taylor & Francis Ltd
Subjects
Boundary control
Control theory
disturbances estimator
Initial conditions
Mathematical analysis
Neumann boundary control
prescribed-time stabilisation
Reaction-diffusion equations
time-varying feedback gain
Uncertainty
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ISSN0020-7179
1366-5820
DOI10.1080/00207179.2022.2094837

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Summary:We study the Neumann boundary feedback stabilisation for reaction-diffusion equations with matched boundary uncertainties (including internal uncertainty and external disturbance) within a prescribed time, where the convergence time is independent of initial conditions and can be prescribed a priori. We first estimate the uncertainties within the prescribed time by constructing an estimator and then propose the prescribed-time boundary control law by utilising backstepping transformation with a time-varying kernel. Neumann boundary control is verified to be uniformly bounded.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2022.2094837