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Title: Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions

Creator:

Armaou, Antonios ; Christofides, Panagiotis D.

Date:

2001

Resource Type:

artykuł

Contributor:

Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.

Group publication title:

AMCS, volume 11 (2001)

Abstract:

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. ; Then, the Karhunen-Loéve expansion is directly applied to the ensemble of solutions to derive a small set of empirical eigenfunctions (dominant spatial patterns) that capture almost all the energy of the ensemble of solutions. The empirical eigenfunctions are subsequently used as basis functions within a Galerkin model reduction framework to derive loworder ordinary differential equation (ODE) systems that accurately describe the dominant dynamics of the PDE system. The ODE systems are subsequently used for the synthesis of nonlinear output feedback controllers using geometric control methods. ; The proposed control method is used to stabilize an unstable steady-state of a diffusion-reaction process with nonlinearities, spatially-varying coeffcients and time-dependent spatial domain, and is shown to lead to the construction of accurate low-order models and the synthesis of low-order controllers. The performance of the low-order models and controllers is successfully tested through computer simulations.

Publisher:

Zielona Góra: Uniwersytet Zielonogórski

Resource Identifier:

oai:zbc.uz.zgora.pl:58766

Pages:

287-317

Source:

AMCS, volume 11, number 2 (2001) ; click here to follow the link

Language:

eng

Rights:

Biblioteka Uniwersytetu Zielonogórskiego

Subject and keywords:

Karhunen-Loéve expansion Galerkin's method nonlinear control diffusion-reaction processes with moving boundaries

Object collections:

Last modified:

Nov 5, 2024

In our library since:

Jul 20, 2021

Number of object content hits:

121

All available object's versions:

https://zbc.uz.zgora.pl/publication/65548

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Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions Nov 5, 2024

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