Boundary control of long waves in nonlinear dispersive systems

Agus Hasan, Bjarne Foss, Ole Morten Aamo

Publikation: Bidrag til bog/antologi/rapport/konference-proceedingKonferencebidrag i proceedingsForskningpeer review

Resumé

Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases.
OriginalsprogEngelsk
TitelProceedings of the 2011 Australian Control Conference
ForlagIEEE
Publikationsdato2011
Sider230-235
StatusUdgivet - 2011
Udgivet eksterntJa
BegivenhedThe 2011 Australian Control Conference - Melbourne, Australien
Varighed: 10. nov. 201111. nov. 2011

Konference

KonferenceThe 2011 Australian Control Conference
LandAustralien
ByMelbourne
Periode10/11/201111/11/2011

Fingeraftryk

Global Exponential Stability
Boundary Control
Mixed partial derivative
Nonlinearity
Third Order Differential Equation
Solitary Wave Solution
Nonlinear Waves
Nonlinear Control
Term
Burgers Equation
Trivial
Covering
Partial differential equation
Unstable
Propagation
Higher Order

Citer dette

Hasan, A., Foss, B., & Aamo, O. M. (2011). Boundary control of long waves in nonlinear dispersive systems. I Proceedings of the 2011 Australian Control Conference (s. 230-235). IEEE.
Hasan, Agus ; Foss, Bjarne ; Aamo, Ole Morten. / Boundary control of long waves in nonlinear dispersive systems. Proceedings of the 2011 Australian Control Conference. IEEE, 2011. s. 230-235
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author = "Agus Hasan and Bjarne Foss and Aamo, {Ole Morten}",
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Hasan, A, Foss, B & Aamo, OM 2011, Boundary control of long waves in nonlinear dispersive systems. i Proceedings of the 2011 Australian Control Conference. IEEE, s. 230-235, The 2011 Australian Control Conference, Melbourne, Australien, 10/11/2011.

Boundary control of long waves in nonlinear dispersive systems. / Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten.

Proceedings of the 2011 Australian Control Conference. IEEE, 2011. s. 230-235.

Publikation: Bidrag til bog/antologi/rapport/konference-proceedingKonferencebidrag i proceedingsForskningpeer review

TY - GEN

T1 - Boundary control of long waves in nonlinear dispersive systems

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AU - Foss, Bjarne

AU - Aamo, Ole Morten

PY - 2011

Y1 - 2011

N2 - Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases.

AB - Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases.

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EP - 235

BT - Proceedings of the 2011 Australian Control Conference

PB - IEEE

ER -

Hasan A, Foss B, Aamo OM. Boundary control of long waves in nonlinear dispersive systems. I Proceedings of the 2011 Australian Control Conference. IEEE. 2011. s. 230-235