Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions - Armaou, Antonios; Christofides, Panagiotis D. (Zielona Góra: Uniwersytet Zielonogórski)
This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initial conditions and input perturbations) ensemble of solutions of the resulting time-varying PDE system is constructed by computing and solving a high-order discretization of the PDE.
Keywords: Karhunen-Loéve expansion; Galerkin's method; nonlinear control; diffusion-reaction processes with moving boundaries