# A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem

Branislav Rehák; Sergej Čelikovský; Javier Ruiz; Jorge Orozco-Mora

Kybernetika (2009)

- Volume: 45, Issue: 3, page 427-444
- ISSN: 0023-5954

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topRehák, Branislav, et al. "A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem." Kybernetika 45.3 (2009): 427-444. <http://eudml.org/doc/37676>.

@article{Rehák2009,

abstract = {The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper presents two methods to handle the algebraic condition: the first one is based on iterative minimization of a cost functional defined as the integral of the square of the algebraic expression to be equal to zero. The second method converts the algebraic-differential equation into a singularly perturbed system of partial differential equations only. Both methods are compared and the simulation results are presented including on-line control implementation to some practically motivated laboratory models.},

author = {Rehák, Branislav, Čelikovský, Sergej, Ruiz, Javier, Orozco-Mora, Jorge},

journal = {Kybernetika},

keywords = {nonlinear output regulation; singularly perturbed equation; gyroscope; nonlinear output regulation; singularly perturbed equation; gyroscope},

language = {eng},

number = {3},

pages = {427-444},

publisher = {Institute of Information Theory and Automation AS CR},

title = {A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem},

url = {http://eudml.org/doc/37676},

volume = {45},

year = {2009},

}

TY - JOUR

AU - Rehák, Branislav

AU - Čelikovský, Sergej

AU - Ruiz, Javier

AU - Orozco-Mora, Jorge

TI - A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem

JO - Kybernetika

PY - 2009

PB - Institute of Information Theory and Automation AS CR

VL - 45

IS - 3

SP - 427

EP - 444

AB - The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper presents two methods to handle the algebraic condition: the first one is based on iterative minimization of a cost functional defined as the integral of the square of the algebraic expression to be equal to zero. The second method converts the algebraic-differential equation into a singularly perturbed system of partial differential equations only. Both methods are compared and the simulation results are presented including on-line control implementation to some practically motivated laboratory models.

LA - eng

KW - nonlinear output regulation; singularly perturbed equation; gyroscope; nonlinear output regulation; singularly perturbed equation; gyroscope

UR - http://eudml.org/doc/37676

ER -

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- [unknown], J. Ruiz-León, J. L. Orozco-Mora, and D. Henrion: Real-time and control of a gyroscope using Polynomial Toolbox 2.5. In: Latin-American Conference on Automatic Control CLCA 2002, Guadalajara 2002.
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