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Artículos de revistas sobre el tema "Global exact boundary controllability"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 8 de febrero de 2022

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1

CHAPOULY, MARIANNE. "GLOBAL CONTROLLABILITY OF A NONLINEAR KORTEWEG–DE VRIES EQUATION". Communications in Contemporary Mathematics 11, n.º 03 (junio de 2009): 495–521. http://dx.doi.org/10.1142/s0219199709003454.

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We are interested in both the global exact controllability to the trajectories and in the global exact controllability of a nonlinear Korteweg–de Vries equation in a bounded interval. The local exact controllability to the trajectories by means of one boundary control, namely the boundary value at the left endpoint, has already been proved independently by Rosier, and Glass and Guerrero. We first introduce here two more controls: the boundary value at the right endpoint and the right member of the equation, assumed to be x-independent. Then, we prove that, thanks to these three controls, one has the global exact controllability to the trajectories, for any positive time T. Finally, we introduce a fourth control on the first derivative at the right endpoint, and we get the global exact controllability, for any positive time T.

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2

Araújo, Raul K. C., Enrique Fernández-Cara y Diego A. Souza. "On the uniform controllability for a family of non-viscous and viscous Burgers-α systems". ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 78. http://dx.doi.org/10.1051/cocv/2021073.

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In this paper we study the global controllability of families of the so called non-viscous and viscous Burgers-α systems by using boundary and space independent distributed controls. In these equations, the usual convective velocity of the Burgers equation is replaced by a regularized velocity, induced by a Helmholtz filter of characteristic wavelength α. First, we prove a global exact controllability result (uniform with respect to α) for the non-viscous Burgers-α system, using the return method and a fixed-point argument. Then, the global uniform exact controllability to constant states is deduced for the viscous equations. To this purpose, we first prove a local exact controllability property and, then, we establish a global approximate controllability result for smooth initial and target states.

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3

Li (Daqian Li), Tatsien. "Global exact boundary controllability for first order quasilinear hyperbolic systems". Discrete & Continuous Dynamical Systems - B 14, n.º 4 (2010): 1419–32. http://dx.doi.org/10.3934/dcdsb.2010.14.1419.

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4

Wang, Ke. "Global exact boundary controllability for 1-D quasilinear wave equations". Mathematical Methods in the Applied Sciences 34, n.º 3 (23 de agosto de 2010): 315–24. http://dx.doi.org/10.1002/mma.1358.

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5

Li, Tatsien y Lei Yu. "Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws". ESAIM: Control, Optimisation and Calculus of Variations 24, n.º 2 (abril de 2018): 793–810. http://dx.doi.org/10.1051/cocv/2017072.

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In this paper, we study the local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws with characteristics of constant multiplicity. We prove the two-sided boundary controllability, the one-sided boundary controllability and the two-sided boundary controllability with fewer controls, by applying the strategy used in [T. Li and L. Yu, J. Math. Pures et Appl. 107 (2017) 1–40; L. Yu, Chinese Ann. Math., Ser. B (To appear)]. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions, and on some further properties of both ε-approximate front tracking solutions and limit solutions.

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6

Liu, Cunming y Peng Qu. "Global exact boundary controllability for general first-order quasilinear hyperbolic systems". Chinese Annals of Mathematics, Series B 36, n.º 6 (25 de octubre de 2015): 895–906. http://dx.doi.org/10.1007/s11401-015-0968-7.

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7

Capistrano–Filho, Roberto A., Ademir F. Pazoto y Lionel Rosier. "Control of a Boussinesq system of KdV–KdV type on a bounded interval". ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 58. http://dx.doi.org/10.1051/cocv/2018036.

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We consider a Boussinesq system of KdV–KdV type introduced by J.L. Bona, M. Chen and J.-C. Saut as a model for the motion of small amplitude long waves on the surface of an ideal fluid. This system of two equations can describe the propagation of waves in both directions, while the single KdV equation is limited to unidirectional waves. We are concerned here with the exact controllability of the Boussinesq system by using some boundary controls. By reducing the controllability problem to a spectral problem which is solved by using the Paley–Wiener method introduced by the third author for KdV, we determine explicitly all the critical lengths for which the exact controllability fails for the linearized system, and give a complete picture of the controllability results with one or two boundary controls of Dirichlet or Neumann type. The extension of the exact controllability to the full Boussinesq system is derived in the energy space in the case of a control of Neumann type. It is obtained by incorporating a boundary feedback in the control in order to ensure a global Kato smoothing effect.

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8

Yin, Zhongqi. "Null exact controllability of the parabolic equations with equivalued surface boundary condition". Journal of Applied Mathematics and Stochastic Analysis 2006 (13 de abril de 2006): 1–10. http://dx.doi.org/10.1155/jamsa/2006/62694.

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This paper is devoted to showing the null exact controllability for a class of parabolic equations with equivalued surface boundary condition. Our method is based on the duality argument and global Carleman-type estimate for a parabolic operator.

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9

CORON, JEAN-MICHEL y EMMANUEL TRÉLAT. "GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS". Communications in Contemporary Mathematics 08, n.º 04 (agosto de 2006): 535–67. http://dx.doi.org/10.1142/s0219199706002209.

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This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an expansion of the solution in a one-parameter Riesz basis of generalized eigenvectors, and on an effective feedback stabilization procedure which is implemented.

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10

Li, Tatsien y Zhiqiang Wang. "Global exact boundary controllability for first order quasilinear hyperbolic systems of diagonal form". International Journal of Dynamical Systems and Differential Equations 1, n.º 1 (2007): 12. http://dx.doi.org/10.1504/ijdsde.2007.013741.

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11

Gugat, Martin. "Exact Boundary Controllability for Free Traffic Flow with Lipschitz Continuous State". Mathematical Problems in Engineering 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/2743251.

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We consider traffic flow governed by the LWR model. We show that a Lipschitz continuous initial density with free-flow and sufficiently small Lipschitz constant can be controlled exactly to an arbitrary constant free-flow density in finite time by a piecewise linear boundary control function that controls the density at the inflow boundary if the outflow boundary is absorbing. Moreover, this can be done in such a way that the generated state is Lipschitz continuous. Since the target states need not be close to the initial state, our result is a global exact controllability result. The Lipschitz constant of the generated state can be made arbitrarily small if the Lipschitz constant of the initial density is sufficiently small and the control time is sufficiently long. This is motivated by the idea that finite or even small Lipschitz constants are desirable in traffic flow since they might help to decrease the speed variation and lead to safer traffic.

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12

Vergara-Hermosilla, G., G. Leugering y Y. Wang. "Boundary controllability of a system modelling a partially immersed obstacle". ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 80. http://dx.doi.org/10.1051/cocv/2021076.

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In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In particular, we use the concept of nodal profile controllability in which at a given point (the node) time-dependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the semi-global classical solutions of the system, then get the local controllability and nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving these control problem.

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13

Kong, De-Xing. "Global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws". Systems & Control Letters 47, n.º 4 (noviembre de 2002): 287–98. http://dx.doi.org/10.1016/s0167-6911(02)00200-1.

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14

Zhou, Yi, Wei Xu y Zhen Lei. "Global exact boundary controllability for cubic semi-linear wave equations and Klein-Gordon equations". Chinese Annals of Mathematics, Series B 31, n.º 1 (11 de diciembre de 2009): 35–58. http://dx.doi.org/10.1007/s11401-008-0426-x.

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15

Kim, Tujin, Qian-shun Chang y Jing Xu. "A global Carleman inequality and exact controllability of parabolic equations with mixed boundary conditions". Acta Mathematicae Applicatae Sinica, English Series 24, n.º 2 (abril de 2008): 265–80. http://dx.doi.org/10.1007/s10255-006-6011-8.

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16

Kong, De-Xing y Hui Yao. "Global Exact Boundary Controllability of a Class of Quasilinear Hyperbolic Systems of Conservation Laws II". SIAM Journal on Control and Optimization 44, n.º 1 (enero de 2005): 140–58. http://dx.doi.org/10.1137/s0363012903432651.

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17

Coron, Jean-Michel, Frédéric Marbach y Franck Sueur. "Small-time global exact controllability of the Navier–Stokes equation with Navier slip-with-friction boundary conditions". Journal of the European Mathematical Society 22, n.º 5 (11 de febrero de 2020): 1625–73. http://dx.doi.org/10.4171/jems/952.

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18

Avdonin, Sergei, Abdon Choque Rivero y Luz De Teresa. "Exact boundary controllability of coupled hyperbolic equations". International Journal of Applied Mathematics and Computer Science 23, n.º 4 (1 de diciembre de 2013): 701–9. http://dx.doi.org/10.2478/amcs-2013-0052.

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Abstract We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.

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19

Aassila, Mohammed. "Exact boundary controllability of a coupled system". Discrete and Continuous Dynamical Systems 6, n.º 3 (abril de 2000): 665–72. http://dx.doi.org/10.3934/dcds.2000.6.665.

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20

Weck, N. "Exact Boundary Controllability of a Maxwell Problem". SIAM Journal on Control and Optimization 38, n.º 3 (enero de 2000): 736–50. http://dx.doi.org/10.1137/s0363012998347559.

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21

Leugering, G�nter. "Exact boundary controllability of an integrodifferential equation". Applied Mathematics & Optimization 15, n.º 1 (enero de 1987): 223–50. http://dx.doi.org/10.1007/bf01442653.

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22

Guzmán, Patricio y Jiamin Zhu. "Exact boundary controllability of a microbeam model". Journal of Mathematical Analysis and Applications 425, n.º 2 (mayo de 2015): 655–65. http://dx.doi.org/10.1016/j.jmaa.2014.12.059.

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23

Tatsien, Li. "Exact boundary controllability for quasilinear wave equations". Journal of Computational and Applied Mathematics 190, n.º 1-2 (junio de 2006): 127–35. http://dx.doi.org/10.1016/j.cam.2005.04.012.

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24

Lasri, Marieme, Hamid Bounit y Said Hadd. "On exact controllability of linear perturbed boundary systems: a semigroup approach". IMA Journal of Mathematical Control and Information 37, n.º 4 (12 de octubre de 2020): 1548–73. http://dx.doi.org/10.1093/imamci/dnaa024.

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Abstract The purpose of this paper is to investigate the robustness of exact controllability of perturbed linear systems in Banach spaces. Under some conditions, we prove that the exact controllability is preserved if we perturb the generator of an infinite-dimensional control system by appropriate Miyadera–Voigt perturbations. Furthermore, we study the robustness of exact controllability for perturbed boundary control systems. As application, we study the robustness of exact controllability of neutral equations. We mention that our approach is mainly based on the concept of feedback theory of infinite-dimensional linear systems.

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25

Sadkowski, Wawrzyniec. "GLOBAL EXACT CONTROLLABILITY FOR GENERALIZED WAVE EQUATION". Demonstratio Mathematica 30, n.º 3 (1 de julio de 1997): 687–96. http://dx.doi.org/10.1515/dema-1997-0326.

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26

Engel, Klaus-Jochen y Marjeta Kramar FijavŽ. "Exact and positive controllability of boundary control systems". Networks & Heterogeneous Media 12, n.º 2 (2017): 319–37. http://dx.doi.org/10.3934/nhm.2017014.

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27

Zhou, Yi y Zhen Lei. "Local Exact Boundary Controllability for Nonlinear Wave Equations". SIAM Journal on Control and Optimization 46, n.º 3 (enero de 2007): 1022–51. http://dx.doi.org/10.1137/060650222.

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28

Rajaram, Rajeev. "Exact boundary controllability of the linear advection equation". Applicable Analysis 88, n.º 1 (enero de 2009): 121–29. http://dx.doi.org/10.1080/00036810802713842.

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29

Li, Ta-Tsien y Bo-Peng Rao. "Exact Boundary Controllability for Quasi-Linear Hyperbolic Systems". SIAM Journal on Control and Optimization 41, n.º 6 (enero de 2003): 1748–55. http://dx.doi.org/10.1137/s0363012901390099.

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30

Kapitonov, B. V. "Stabilization and Exact Boundary Controllability for Maxwell’s Equations". SIAM Journal on Control and Optimization 32, n.º 2 (marzo de 1994): 408–20. http://dx.doi.org/10.1137/s0363012991218487.

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31

Fursikov, A. V. y O. Yu Imanuvilov. "Local Exact Boundary Controllability of the Boussinesq Equation". SIAM Journal on Control and Optimization 36, n.º 2 (marzo de 1998): 391–421. http://dx.doi.org/10.1137/s0363012996296796.

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32

Glass, Olivier. "Exact boundary controllability of 3-D Euler equation". ESAIM: Control, Optimisation and Calculus of Variations 5 (2000): 1–44. http://dx.doi.org/10.1051/cocv:2000100.

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33

Rosier, Lionel y Bing-Yu Zhang. "Exact boundary controllability of the nonlinear Schrödinger equation". Journal of Differential Equations 246, n.º 10 (mayo de 2009): 4129–53. http://dx.doi.org/10.1016/j.jde.2008.11.004.

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34

Antunes, G. O., M. D. G. da Silva y R. F. Apolaya. "Schrödinger equations in noncylindrical domains: exact controllability". International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–29. http://dx.doi.org/10.1155/ijmms/2006/78192.

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We consider an open bounded setΩ⊂ℝnand a family{K(t)}t≥0of orthogonal matrices ofℝn. SetΩt={x∈ℝn;x=K(t)y,for all y∈Ω}, whose boundary isΓt. We denote byQ^the noncylindrical domain given byQ^=∪0<t<T{Ωt×{t}}, with the regular lateral boundaryΣ^=∪0<t<T{Γt×{t}}. In this paper we investigate the boundary exact controllability for the linear Schrödinger equationu′−iΔu=finQ^(i2=−1),u=wonΣ^,u(x,0)=u0(x)inΩ0, wherewis the control.

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35

BRADLEY, MARY E. y IRENA LASIECKA. "EXACT BOUNDARY CONTROLLABILITY OF A NONLINEAR SHALLOW SPHERICAL SHELL". Mathematical Models and Methods in Applied Sciences 08, n.º 06 (septiembre de 1998): 927–55. http://dx.doi.org/10.1142/s0218202598000421.

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We consider the problem of boundary exact controllability of a coupled nonlinear system which describes vibrations of a thin, shallow, spherical shell. We show that under the geometric condition of "shallowness", which restricts the curvature with respect to the thickness, the system is exactly controllable in the natural "finite energy" space by means of L2 controls. This controllability is produced via moments and shear forces applied to the edge of the shell.

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36

Hu, Long, Fanqiong Ji y Ke Wang. "Exact boundary controllability and exact boundary observability for a coupled system of quasilinear wave equations". Chinese Annals of Mathematics, Series B 34, n.º 4 (julio de 2013): 479–90. http://dx.doi.org/10.1007/s11401-013-0785-9.

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37

Fabre, Caroline. "Exact Boundary Controllability of the Wave Equation as the Limit of Internal Controllability". SIAM Journal on Control and Optimization 30, n.º 5 (septiembre de 1992): 1066–86. http://dx.doi.org/10.1137/0330056.

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38

Li, Ta-Tsien y Yu-Lan Xu. "Local Exact Boundary Controllability for Nonlinear Vibrating String Equations". International Journal of Modern Physics B 17, n.º 22n24 (30 de septiembre de 2003): 4062–71. http://dx.doi.org/10.1142/s0217979203022039.

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Based on the theory of semiglobal C1 solutions to a class of nonlocal mixed initial-boundary value problems for quasilinear hyperbolic systems, we establish the local exact boundary controllability for a class of nonlinear vibrating string problems with boundary condition of the third type on one end.

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39

Liu, Weijiu y Graham Williams. "Exact Neumann boundary controllability for second order hyperbolic equations". Colloquium Mathematicum 76, n.º 1 (1998): 117–42. http://dx.doi.org/10.4064/cm-76-1-117-142.

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40

Karite, Touria y Ali Boutoulout. "Boundary gradient exact enlarged controllability of semilinear parabolic problems". Advances in Science, Technology and Engineering Systems Journal 2, n.º 5 (diciembre de 2017): 167–72. http://dx.doi.org/10.25046/aj020524.

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41

Santos, Manoel J., Carlos A. Raposo y Leonardo R. S. Rodrigues. "Boundary exact controllability for a porous elastic Timoshenko system". Applications of Mathematics 65, n.º 4 (3 de julio de 2020): 343–54. http://dx.doi.org/10.21136/am.2020.0133-19.

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42

Bastos, W. D., A. Spezamiglio y C. A. Raposo. "On exact boundary controllability for linearly coupled wave equations". Journal of Mathematical Analysis and Applications 381, n.º 2 (septiembre de 2011): 557–64. http://dx.doi.org/10.1016/j.jmaa.2011.02.074.

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43

Rodrigues, Sérgio S. "Local exact boundary controllability of 3D Navier–Stokes equations". Nonlinear Analysis: Theory, Methods & Applications 95 (enero de 2014): 175–90. http://dx.doi.org/10.1016/j.na.2013.09.003.

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44

Tatsien, Li y Yu Lixin. "Exact Boundary Controllability for 1‐D Quasilinear Wave Equations". SIAM Journal on Control and Optimization 45, n.º 3 (enero de 2006): 1074–83. http://dx.doi.org/10.1137/s0363012903427300.

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45

Zhang, Bing-Yu. "Exact Boundary Controllability of the Korteweg--de Vries Equation". SIAM Journal on Control and Optimization 37, n.º 2 (enero de 1999): 543–65. http://dx.doi.org/10.1137/s0363012997327501.

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46

Zhang, Chun-Guo y Hong-Xiang Hu. "Exact controllability of a Timoshenko beam with dynamical boundary". Journal of Mathematics of Kyoto University 47, n.º 3 (2007): 643–55. http://dx.doi.org/10.1215/kjm/1250281029.

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47

Wang, Zhiqiang. "Exact boundary controllability for non-autonomous quasilinear wave equations". Mathematical Methods in the Applied Sciences 30, n.º 11 (2007): 1311–27. http://dx.doi.org/10.1002/mma.843.

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48

Lixin, Yu. "Exact boundary controllability for higher order quasilinear hyperbolic equations". Applied Mathematics-A Journal of Chinese Universities 20, n.º 2 (junio de 2005): 127–41. http://dx.doi.org/10.1007/s11766-005-0045-1.

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49

Zong, Xiju, Yi Zhao, Zhaoyang Yin y Tao Chi. "Exact boundary controllability of 1-D nonlinear Schrödinger equation". Applied Mathematics-A Journal of Chinese Universities 22, n.º 3 (septiembre de 2007): 277–85. http://dx.doi.org/10.1007/s11766-007-0304-4.

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50

Kapitonov, B. V. "Uniqueness theorems and exact boundary controllability of evolution systems". Siberian Mathematical Journal 34, n.º 5 (1993): 852–68. http://dx.doi.org/10.1007/bf00971402.

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