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

Yilmaz Turkyilmaz, Jerome Jouffroy, Olav Egeland

Publikation: Konferencebidrag uden forlag/tidsskriftPaperForskningpeer review

Resumé

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.
OriginalsprogEngelsk
Publikationsdato2004
StatusUdgivet - 2004
Begivenhed IFAC Conference on Control Applications in Marine Systems (CAMS'04) - Ancona, Italien
Varighed: 24. aug. 2010 → …

Konference

Konference IFAC Conference on Control Applications in Marine Systems (CAMS'04)
LandItalien
ByAncona
Periode24/08/2010 → …

Fingeraftryk

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

Citer dette

Turkyilmaz, Y., Jouffroy, J., & Egeland, O. (2004). Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory. Afhandling præsenteret på  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italien.
Turkyilmaz, Yilmaz ; Jouffroy, Jerome ; Egeland, Olav. / Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory. Afhandling præsenteret på  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italien.
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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 fremlagt ved  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italien, 24/08/2010, .

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

2004. Afhandling præsenteret på  IFAC Conference on Control Applications in Marine Systems (CAMS'04), Ancona, Italien.

Publikation: Konferencebidrag uden forlag/tidsskriftPaperForskningpeer 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

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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

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