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| 2. |
- Kelleche, Abdelkarim, et al.
(författare)
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On stabilization of an axially moving string with a tip mass subject to an unbounded disturbance
- 2023
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Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476.
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with the stabilization problem of an axially moving string with a tip mass attached at the free end and subject to an external disturbance. The disturbance here is not uniformly bounded, and it is assumed to be exponentially increasing. First, the tip mass equation is designed under a boundary controller. By using this equation, the active disturbance rejection control (ADRC) technique is applied to design a disturbance observer, and it is shown that the observer can be estimated exponentially. Then, the closed-loop system is formulated and the well-posedness of the model is proved in the framework of the semigroup theory. The stability of the closed-loop system is then proved by means of the multiplier technique, where the energy system converges to equilibrium with an exponential manner. The efficiency of the obtained results is verified through numerical simulations.
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| 3. |
- Kelleche, Abdelkarim, et al.
(författare)
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Stabilization of an Axially Moving Euler Bernoulli Beam by an Adaptive Boundary Control
- 2023
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Ingår i: Journal of dynamical and control systems. - : Springer Science and Business Media LLC. - 1079-2724 .- 1573-8698.
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns with the stabilization of an axially moving beam by an adaptive boundary control. We prove existence and uniqueness of the solution by means of nonlinear semigroup theory. Moreover, we construct the control through a low-gain adaptive velocity feedback. We also prove that the designed control is able to stabilize exponentially the closed loop system. Some numerical simulations are given to illustrate the theoretical results.
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| 4. |
- Kelleche, Abdelkarim, et al.
(författare)
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Stabilization of an axially moving viscoelastic string under a spatiotemporally varying tension
- 2018
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Ingår i: Mathematical methods in the applied sciences. - : Wiley. - 0170-4214 .- 1099-1476. ; 41:17, s. 7852-7868
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider a system modeling an axially moving viscoelastic string under a spatiotemporally varying tension. A mechanism consisted of a hydraulic touch-roll actuator pointed at the right boundary to suppress the transverse vibrations. We adopt the multiplier method to design a boundary control law and to prove an exponential stability result. However, this result is obtained provided that the lower bound of the tension in the string is larger than its time derivative. The effectiveness of the proposed control law is demonstrated via simulations.
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| 5. |
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| 6. |
- Kovacs, Mihaly, 1977, et al.
(författare)
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Finite element approximation of the linear stochastic wave equation with additive noise
- 2010
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 48:2, s. 408-427
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Tidskriftsartikel (refereegranskat)abstract
- Semidiscrete finite element approximation of the linear stochastic wave equation (LSWE) with additive noise is studied in a semigroup framework. Optimal error estimates for the deterministic problem are obtained under minimal regularity assumptions. These are used to prove strong convergence estimates for the stochastic problem. The theory presented here applies to multidimensional domains and spatially correlated noise. Numerical examples illustrate the theory.
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| 7. |
- Kovacs, Mihaly, 1977, et al.
(författare)
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Mittag-leffler euler integrator for a stochastic fractional order equation with additive noise
- 2020
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Ingår i: SIAM Journal on Numerical Analysis. - 0036-1429 .- 1095-7170. ; 58:1, s. 66-85
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here the Mittag-Leffler Euler integrator, is used for the temporal discretization, while the spatial discretization is performed by the spectral Galerkin method. The temporal rate of strong convergence is found to be (almost) twice compared to when the backward Euler method is used together with a convolution quadrature for time discretization. Numerical experiments that validate the theory are presented. © 2020 Society for Industrial and Applied Mathematics.
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| 8. |
- Kovács, Mihály, et al.
(författare)
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Mittag-Leffler Euler integrator for a stochastic fractional order equation with additive noise
- 2020
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Ingår i: SIAM Journal on Numerical Analysis. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1429 .- 1095-7170. ; 58:1, s. 66-85
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here the Mittag--Leffler Euler integrator, is used for the temporal discretization, while the spatial discretization is performed by the spectral Galerkin method. The temporal rate of strong convergence is found to be (almost) twice compared to when the backward Euler method is used together with a convolution quadrature for time discretization. Numerical experiments that validate the theory are presented.
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| 9. |
- Larsson, Stig, 1952, et al.
(författare)
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Discontinuous Galerkin method for an integro-differential equation modeling dynamic fractional order viscoelasticity
- 2015
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 283, s. 196-209
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Tidskriftsartikel (refereegranskat)abstract
- An integro-differential equation, modeling dynamic fractional order viscoelasticity, with a Mittag-Leffler type convolution kernel is considered. A discontinuous Galerkin method, based on piecewise constant polynomials, is formulated for temporal semidiscretization of the problem. Stability estimates of the discrete problem are proved, that are used to prove optimal order a priori error estimates. The theory is illustrated by a numerical example.
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| 10. |
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