Asymptotic output tracking for a class of semilinear parabolic equations: A semianalytical approach

Summary This paper addresses the problem of asymptotic output tracking of a class of semilinear parabolic equations with pointwise in‐domain actuation. First, the assessment of the well‐posedness of the considered systems is performed, and then, the stability of boundary controlled systems is analyz...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2019-05, Vol.29 (8), p.2471-2493
Main Authors: Yang, Kaijun, Zheng, Jun, Zhu, Guchuan
Format: Article
Language:English
Subjects:
Actuation
Adomian decomposition method
Asymptotic properties
Computer simulation
Control stability
Convergence
Cybernetics
differential flatness
Dynamic control
Inverse design
Mathematical analysis
semilinear parabolic equations
Stability analysis
Tracking
Trajectory planning
zero dynamics
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Summary:Summary This paper addresses the problem of asymptotic output tracking of a class of semilinear parabolic equations with pointwise in‐domain actuation. First, the assessment of the well‐posedness of the considered systems is performed, and then, the stability of boundary controlled systems is analyzed via Chaffee‐Infante equation and Fisher's equation. The application of the zero dynamics inverse design results in a dynamic control scheme that is implemented by using the technique of trajectory planning for flat systems and the Adomian decomposition method. The convergence of the solution of the original systems to that of the corresponding zero dynamics and the convergence of the solution expressed by an Adomian series are also analyzed. Numerical simulations are carried out to illustrate the effectiveness of the developed approach.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.4504