Wave Equation With Cone-Bounded Control Laws
This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kin...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Prieur, Christophe [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2016 |
|---|
| Schlagwörter: |
nonlinear partial differential equations |
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| Übergeordnetes Werk: |
Enthalten in: IEEE transactions on automatic control - New York, NY : Inst., 1963, 61(2016), 11, Seite 3452-3463 |
|---|---|
| Übergeordnetes Werk: |
volume:61 ; year:2016 ; number:11 ; pages:3452-3463 |
| Links: |
|---|
| DOI / URN: |
10.1109/TAC.2016.2519759 |
|---|
| Katalog-ID: |
OLC1983986178 |
|---|
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| 520 | |a This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. | ||
| 650 | 4 | |a saturated controls | |
| 650 | 4 | |a nonlinear partial differential equations | |
| 650 | 4 | |a Asymptotic stability | |
| 650 | 4 | |a Closed loop systems | |
| 650 | 4 | |a Infinite dimensional systems | |
| 650 | 4 | |a Aerospace electronics | |
| 650 | 4 | |a Boundary conditions | |
| 650 | 4 | |a Dynamics | |
| 650 | 4 | |a Propagation | |
| 650 | 4 | |a Partial differential equations | |
| 650 | 4 | |a Control systems | |
| 650 | 4 | |a Nonlinear programming | |
| 700 | 1 | |a Tarbouriech, Sophie |4 oth | |
| 700 | 1 | |a Gomes da Silva, Joao M |4 oth | |
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10.1109/TAC.2016.2519759 doi PQ20161201 (DE-627)OLC1983986178 (DE-599)GBVOLC1983986178 (PRQ)c996-4ba3549b25fccdce055673154c54d26468b6750f0aa4b7399aa2dea63ffc79ae0 (KEY)0005057120160000061001103452waveequationwithconeboundedcontrollaws DE-627 ger DE-627 rakwb eng 620 DNB Prieur, Christophe verfasserin aut Wave Equation With Cone-Bounded Control Laws 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. saturated controls nonlinear partial differential equations Asymptotic stability Closed loop systems Infinite dimensional systems Aerospace electronics Boundary conditions Dynamics Propagation Partial differential equations Control systems Nonlinear programming Tarbouriech, Sophie oth Gomes da Silva, Joao M oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 61(2016), 11, Seite 3452-3463 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:61 year:2016 number:11 pages:3452-3463 http://dx.doi.org/10.1109/TAC.2016.2519759 Volltext http://ieeexplore.ieee.org/document/7386612 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 61 2016 11 3452-3463 |
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10.1109/TAC.2016.2519759 doi PQ20161201 (DE-627)OLC1983986178 (DE-599)GBVOLC1983986178 (PRQ)c996-4ba3549b25fccdce055673154c54d26468b6750f0aa4b7399aa2dea63ffc79ae0 (KEY)0005057120160000061001103452waveequationwithconeboundedcontrollaws DE-627 ger DE-627 rakwb eng 620 DNB Prieur, Christophe verfasserin aut Wave Equation With Cone-Bounded Control Laws 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. saturated controls nonlinear partial differential equations Asymptotic stability Closed loop systems Infinite dimensional systems Aerospace electronics Boundary conditions Dynamics Propagation Partial differential equations Control systems Nonlinear programming Tarbouriech, Sophie oth Gomes da Silva, Joao M oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 61(2016), 11, Seite 3452-3463 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:61 year:2016 number:11 pages:3452-3463 http://dx.doi.org/10.1109/TAC.2016.2519759 Volltext http://ieeexplore.ieee.org/document/7386612 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 61 2016 11 3452-3463 |
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10.1109/TAC.2016.2519759 doi PQ20161201 (DE-627)OLC1983986178 (DE-599)GBVOLC1983986178 (PRQ)c996-4ba3549b25fccdce055673154c54d26468b6750f0aa4b7399aa2dea63ffc79ae0 (KEY)0005057120160000061001103452waveequationwithconeboundedcontrollaws DE-627 ger DE-627 rakwb eng 620 DNB Prieur, Christophe verfasserin aut Wave Equation With Cone-Bounded Control Laws 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. saturated controls nonlinear partial differential equations Asymptotic stability Closed loop systems Infinite dimensional systems Aerospace electronics Boundary conditions Dynamics Propagation Partial differential equations Control systems Nonlinear programming Tarbouriech, Sophie oth Gomes da Silva, Joao M oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 61(2016), 11, Seite 3452-3463 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:61 year:2016 number:11 pages:3452-3463 http://dx.doi.org/10.1109/TAC.2016.2519759 Volltext http://ieeexplore.ieee.org/document/7386612 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 61 2016 11 3452-3463 |
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10.1109/TAC.2016.2519759 doi PQ20161201 (DE-627)OLC1983986178 (DE-599)GBVOLC1983986178 (PRQ)c996-4ba3549b25fccdce055673154c54d26468b6750f0aa4b7399aa2dea63ffc79ae0 (KEY)0005057120160000061001103452waveequationwithconeboundedcontrollaws DE-627 ger DE-627 rakwb eng 620 DNB Prieur, Christophe verfasserin aut Wave Equation With Cone-Bounded Control Laws 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. saturated controls nonlinear partial differential equations Asymptotic stability Closed loop systems Infinite dimensional systems Aerospace electronics Boundary conditions Dynamics Propagation Partial differential equations Control systems Nonlinear programming Tarbouriech, Sophie oth Gomes da Silva, Joao M oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 61(2016), 11, Seite 3452-3463 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:61 year:2016 number:11 pages:3452-3463 http://dx.doi.org/10.1109/TAC.2016.2519759 Volltext http://ieeexplore.ieee.org/document/7386612 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 61 2016 11 3452-3463 |
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10.1109/TAC.2016.2519759 doi PQ20161201 (DE-627)OLC1983986178 (DE-599)GBVOLC1983986178 (PRQ)c996-4ba3549b25fccdce055673154c54d26468b6750f0aa4b7399aa2dea63ffc79ae0 (KEY)0005057120160000061001103452waveequationwithconeboundedcontrollaws DE-627 ger DE-627 rakwb eng 620 DNB Prieur, Christophe verfasserin aut Wave Equation With Cone-Bounded Control Laws 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. saturated controls nonlinear partial differential equations Asymptotic stability Closed loop systems Infinite dimensional systems Aerospace electronics Boundary conditions Dynamics Propagation Partial differential equations Control systems Nonlinear programming Tarbouriech, Sophie oth Gomes da Silva, Joao M oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 61(2016), 11, Seite 3452-3463 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:61 year:2016 number:11 pages:3452-3463 http://dx.doi.org/10.1109/TAC.2016.2519759 Volltext http://ieeexplore.ieee.org/document/7386612 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_30 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 61 2016 11 3452-3463 |
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ddc 620 misc saturated controls misc nonlinear partial differential equations misc Asymptotic stability misc Closed loop systems misc Infinite dimensional systems misc Aerospace electronics misc Boundary conditions misc Dynamics misc Propagation misc Partial differential equations misc Control systems misc Nonlinear programming |
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Wave Equation With Cone-Bounded Control Laws |
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Wave Equation With Cone-Bounded Control Laws |
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Prieur, Christophe |
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IEEE transactions on automatic control |
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wave equation with cone-bounded control laws |
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Wave Equation With Cone-Bounded Control Laws |
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This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. |
| abstractGer |
This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. |
| abstract_unstemmed |
This paper deals with a wave equation with a one-dimensional space variable, which describes the dynamics of string deflection. Two kinds of control are considered: a distributed action and a boundary control. It is supposed that the control signal is subject to a cone-bounded nonlinearity. This kind of feedback laws includes (but is not restricted to) saturating inputs. By closing the loop with such a nonlinear control, it is thus obtained a nonlinear partial differential equation, which is the generalization of the classical 1D wave equation. The well-posedness is proven by using nonlinear semigroups techniques. Considering a sector condition to tackle the control nonlinearity and assuming that a tuning parameter has a suitable sign, the asymptotic stability of the closed-loop system is proven by Lyapunov techniques. Some numerical simulations illustrate the asymptotic stability of the closed-loop nonlinear partial differential equations. |
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| title_short |
Wave Equation With Cone-Bounded Control Laws |
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Tarbouriech, Sophie Gomes da Silva, Joao M |
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