Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

Yilmaz Turkyilmaz, Jerome Jouffroy, Olav Egeland

Research output: Contribution to conference without publisher/journalPaperResearchpeer-review

Abstract

Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable configuration. It is shown that the estimated configuration converges exponentially to the actual configuration. Numerical results and simulations are shown to be in agreement with the theoretical results.
Original languageEnglish
Publication date2004
Publication statusPublished - 2004
Event IFAC Conference on Control Applications in Marine Systems (CAMS'04) - Ancona, Italy
Duration: 24. Aug 2010 → …

Conference

Conference IFAC Conference on Control Applications in Marine Systems (CAMS'04)
CountryItaly
CityAncona
Period24/08/2010 → …

Fingerprint

Cables
Finite element method
Nonlinear analysis
Galerkin methods
Ordinary differential equations
Partial differential equations

Cite this

Turkyilmaz, Y., Jouffroy, J., & Egeland, O. (2004). Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory. Paper presented at  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italy.
Turkyilmaz, Yilmaz ; Jouffroy, Jerome ; Egeland, Olav. / Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory. Paper presented at  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italy.
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abstract = "Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable configuration. It is shown that the estimated configuration converges exponentially to the actual configuration. Numerical results and simulations are shown to be in agreement with the theoretical results.",
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Turkyilmaz, Y, Jouffroy, J & Egeland, O 2004, 'Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory', Paper presented at  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italy, 24/08/2010.

Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory. / Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav.

2004. Paper presented at  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italy.

Research output: Contribution to conference without publisher/journalPaperResearchpeer-review

TY - CONF

T1 - Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

AU - Turkyilmaz, Yilmaz

AU - Jouffroy, Jerome

AU - Egeland, Olav

PY - 2004

Y1 - 2004

N2 - Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable configuration. It is shown that the estimated configuration converges exponentially to the actual configuration. Numerical results and simulations are shown to be in agreement with the theoretical results.

AB - Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable configuration. It is shown that the estimated configuration converges exponentially to the actual configuration. Numerical results and simulations are shown to be in agreement with the theoretical results.

M3 - Paper

ER -

Turkyilmaz Y, Jouffroy J, Egeland O. Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory. 2004. Paper presented at  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italy.