Advanced search ?

Object

Download

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 - 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:

Sep 3, 2021

In our library since:

Jul 20, 2021

Number of object content hits:

93

All available object's versions:

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

Show description in RDF format:

RDF

Show description in OAI-PMH format:

OAI-PMH

Edition name Date
Finite-dimensional control of nonlinear parabolic PDE systems with time-dependent spatial domains using empirical eigenfunctions Sep 3, 2021

Objects

Similar
AMCS, volume 9 (1999)
AMCS, volume 9 (1999)

Robust control of nonlinear time-delay systems

Antoniades, Charalambos Christofides, Panagiotis D. Korbicz, Józef - red. Uciński, Dariusz - red.

1999
artykuł
AMCS, volume 9 (1999)
AMCS, volume 9 (1999)

Sub-optimal nonlinear predictive and adaptive control based on the parametric Volterra model

Haber, Robert Bars, Ruth Lengyel, Orsolya Kowalczuk, Zdzisław - red.

1999
artykuł
AMCS, volume 8 (1998)
AMCS, volume 8 (1998)

Distributed output feedback control of two-time-scale hyperbolic PDE systems

Christofides, Panagiotis D. Daoutidis, Prodromos Skliar, Mikhail - red. Ramirez, W. Fred - red.

1998
artykuł
AMCS, Volume 24 (2014)
AMCS, Volume 24 (2014)

Design of a multivariable neural controller for control of a nonlinear MIMO plant

Bańka, Stanisław Dworak, Paweł Jaroszewski, Krzysztof Makowski, Ryszard - ed. Zarzycki, Jan - ed.

2014
artykuł
AMCS, Volume 20 (2010)
AMCS, Volume 20 (2010)

Nonlinear controller design of a ship autopilot

Tomera, Mirosław Korbicz, Józef - red. Uciński, Dariusz - red.

2010
artykuł
AMCS, Volume 23 (2013)
AMCS, Volume 23 (2013)

Linear adaptive structure for control of a nonlinear MIMO dynamic plant

Bańka, Stanisław Dworak, Paweł Jaroszewski, Krzysztof Korbicz, Józef - red. Uciński, Dariusz - red.

2013
artykuł
AMCS, volume 12 (2002)
AMCS, volume 12 (2002)

Neural network-based NARX models in non-linear adaptive control

Dzieliński, Andrzej Korbicz, Józef - red. Uciński, Dariusz - red.

2002
artykuł
AMCS, volume 11 (2001)
AMCS, volume 11 (2001)

Analysis of an ISOPE-type dual algorithm for optimizing control and nonlinear optimization

Tadej, Wojciech Tatjewski, Piotr Korbicz, Józef - red. Uciński, Dariusz - red.

2001
artykuł
More

Contact details

Address

University Library
al. Wojska Polskiego 71
65-762 Zielona Góra

Phone

(+48) 68 328 21 55

E-Mail

repozytorium@uz.zgora.pl

Visit us!

This page uses 'cookies'. More information