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Asymptotic output tracking for a class of semilinear parabolic equations: A semianalytical approach
Author(s) -
Yang Kaijun,
Zheng Jun,
Zhu Guchuan
Publication year - 2019
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.4504
Subject(s) - adomian decomposition method , mathematics , convergence (economics) , pointwise , parabolic partial differential equation , boundary (topology) , series (stratigraphy) , exponential stability , control theory (sociology) , trajectory , mathematical analysis , partial differential equation , nonlinear system , control (management) , computer science , paleontology , physics , quantum mechanics , artificial intelligence , astronomy , economics , biology , economic growth
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.