Adaptive boundary control of the unforced generalized Korteweg–de Vries–Burgers equation

Smaoui, Nejib; El-Kadri, Alaa; Zribi, Mohamed

doi:10.1007/s11071-012-0343-0

Cited by 12 publications

(10 citation statements)

References 25 publications

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“…Equation 12is nonlinear because of the 3 rd order partial differential of ( ) V t ∆ with respect to time t. The equation resembles the Korteweg-de Vries (KdV) equation [26] [27] after eliminating the space-dependence, and flipping the space variable with time t. In order for…”

Section: Resultsmentioning

confidence: 99%

Decoupling the Electrical and Entropic Contributions to Energy Transfer from Infrared Radiation to a Power Generator

Gordon¹,

Schwab²,

Lang³

et al. 2015

WJCMP

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The interaction between infrared radiation and a power generator device in time is studied as a route to harvest infrared, and possibly other electromagnetic radiations. Broadening the spectrum of the usable electromagnetic spectrum would greatly contribute to the renewable and sustainable energy sources available to humankind. In particular, low frequency and low power radiation is important for applications on ships, satellites, cars, personal backpacks, and, more generally, where non-dangerous energy is needed at all hours of the day, independent of weather conditions. In this work, we identify an electric and an entropic contribution to the energy transfer from low power infrared radiation to the power generator device, representing electrical and thermal contributions to the power generation. The electric contribution prevails, and is important because it offers multiple ways to increase the voltage produced. For example, placing black-colored gaffer tape on the illuminated face doubles the voltage produced, while the temperature difference, thus the entropic contribution, is not sensitive to the presence of the tape. We recognize the electric contribution through the fast changes it imparts to the voltage output of the power generator device, which mirror the instabilities in time of the infrared radiation. The device thus acts as sensor of the infrared radiation's behavior in time. On the other hand, we distinguish the entropic contribution through the slow changes it causes to the voltage output of the power generator device, which reflect the relative delay with which the two faces of the device respond to thermal perturbations.

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Section: Resultsmentioning

confidence: 99%

Decoupling the Electrical and Entropic Contributions to Energy Transfer from Infrared Radiation to a Power Generator

Gordon¹,

Schwab²,

Lang³

et al. 2015

WJCMP

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show abstract

“…en, the global solutions of the periodic GKdVB equation when α < 4 are obtained and the periodic initial value problem is shown to be well-posed for sufficiently large initial data in the case when α ≥ 4 [33]. In the context of control systems, nonadaptive boundary control laws have been proposed in [38,40,41,42]. Smaoui and Al-Jamal [38] designed three nonadaptive boundary control laws to show that the dynamics of the GKdVB equation is globally exponentially stable in L 2 (0, 1) and globally asymptotically stable and semiglobally exponentially stable in H 1 (0, 1) when α is a positive integer.…”

Section: Introductionmentioning

confidence: 99%

“…Later on, Smaoui et al [40] designed three different nonadaptive boundary control laws, when α is a positive real number, and showed numerically for certain values of α that the proposed controllers outperform those designed in [38]. On the other hand, the adaptive boundary control of the GKdVB equation was discussed in [39,42] when either the kinematic viscosity ν or the dynamic viscosity µ is unknown or when both viscosities ] and µ are unknown.…”

Section: Introductionmentioning

confidence: 99%

“…Up to our knowledge, the adaptive boundary stabilization problem of the MGKdVB equation has not been examined in the literature. In fact, as previously discussed, the adaptive control stabilization of the MGKdVB equation (1) has been dealt with in the following specific cases: μ � c 2 � 0 in [9,12,14,15], c 2 � 0 in [39,42], and μ � 0 in [24].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

2020

Self Cite

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In this paper, we study the nonlinear adaptive boundary control problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) when the spatial domain is 0,1. Four different nonlinear adaptive control laws are designed for the MGKdVB equation without assuming the nullity of the physical parameters ν, μ, γ1, and γ2 and depending whether these parameters are known or unknown. Then, using Lyapunov theory, the L2-global exponential stability of the solution is proven in each case. Finally, numerical simulations are presented to illustrate the developed control schemes.

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“…Quantum control has attracted much attention in recent years and it has been found the potential applications in many fields such as atomic physics [1][2][3][4], molecular chemistry [5][6][7][8][9] and quantum information [10,12]. Up to now, there have been many quantum methods, such as quantum optimal control [13][14][15], adiabatic control [16][17][18], the Lyapunovbased control , and optimal Lyapunov-based quantum control [42]. For the Lyapunov-based quantum control, it is relatively easy to design an analytical but not numerical control law, and the control system based on this control method is at least stable, so it has been a common control method.…”

Section: Introductionmentioning

confidence: 99%

A Survey of Quantum Lyapunov Control Methods

Cong

Meng

2013

The Scientific World Journal

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The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed.

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Adaptive boundary control of the unforced generalized Korteweg–de Vries–Burgers equation

Cited by 12 publications

References 25 publications

Decoupling the Electrical and Entropic Contributions to Energy Transfer from Infrared Radiation to a Power Generator

Decoupling the Electrical and Entropic Contributions to Energy Transfer from Infrared Radiation to a Power Generator

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

A Survey of Quantum Lyapunov Control Methods

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