Finite-dimensional approximation and control of non-linear parabolic PDE systems

By James Baker, Panagiotis D. Christofides. 2000

219 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5ced53a6e7f2c94e01178f44a96d49f3034c0cad

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In Control and Systems Engineering

In Statistical and Nonlinear Physics

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Citations in the corpus

Model-Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges (2021, background): “The question of if infinite dimensional models should be directly used in the design of feedback controllers is a long lasting one, which extends much prior and far beyond the soft robotics field [278], [279].”
Modeling of distributed parameter systems for applications—A synthesized review from time–space separation (2010, unknown): “The applications of KL-Galerkin-AIMmethod [67,68] and the KLcollocationmethod [69–71] are also studied for simulation, control and optimization of thermal processes.”
Predictive control of parabolic PDEs with boundary control actuation (2006, methodology): “…design, dynamic optimization, and the control under actuator saturation—have been addressed for various classes of dissipative PDE systems (e.g., see Baker and Christofides, 2000; Bendersky and Christofides, 2000; Armaou and Christofides, 2002; El-Farra et al., 2003 and the book by Christofides…”
Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions (2001, methodology): “…using empirical eigenfunctions as ba - sis functions in Galerkin ' s method , and a method for the design of nonlinear output feedback controllers for nonlinear parabolic PDE systems was developed in ( Baker and Christofides , 2000 ) by combining Galerkin ' s method with empirical eigenfunctions .”
A spatio-temporal Volterra modeling approach for a class of distributed industrial processes (2009, methodology): “The common used global basis functions include Fourier series [8], orthogonal polynomials [41], eigenfunctions of the system [39,3,11], and data based Karhunen–Loève (KL) empirical eigenfunctions [44,36,30,2], whose choice depends on the type of PDE and boundary conditions.”