Asymptotic output tracking for a class of semilinear parabolic equations: A semianalytical approach. (21st February 2019)

• Record Type: Journal Article
• Authors: Yang, Kaijun; Zheng, Jun; Zhu, Guchuan
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 8(2019)
• Page Start: 2471
• Page End: 2493
• Publication Date: 2019-02-21
• Subjects: Adomian decomposition method -- differential flatness -- semilinear parabolic equations -- zero dynamics; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4504
• Languages: English
• ISSNs: 1049-8923

Abstract

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.