We consider the linear wave equation with Dirichlet boundary conditions in a bounded interval, and with a control acting on a moving point. We give sufficient conditions on the trajectory of the control in order to have the exact controllability property.
Mots-clés : exact controllability, wave equation, pointwise control
@article{COCV_2013__19_1_301_0,
author = {Castro, Carlos},
title = {Exact controllability of the 1-d wave equation from a moving interior point},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {301--316},
publisher = {EDP-Sciences},
volume = {19},
number = {1},
year = {2013},
doi = {10.1051/cocv/2012009},
mrnumber = {3023072},
zbl = {1258.93022},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2012009/}
}
TY - JOUR AU - Castro, Carlos TI - Exact controllability of the 1-d wave equation from a moving interior point JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 301 EP - 316 VL - 19 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012009/ DO - 10.1051/cocv/2012009 LA - en ID - COCV_2013__19_1_301_0 ER -
%0 Journal Article %A Castro, Carlos %T Exact controllability of the 1-d wave equation from a moving interior point %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 301-316 %V 19 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012009/ %R 10.1051/cocv/2012009 %G en %F COCV_2013__19_1_301_0
Castro, Carlos. Exact controllability of the 1-d wave equation from a moving interior point. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 301-316. doi : 10.1051/cocv/2012009. http://www.numdam.org/articles/10.1051/cocv/2012009/
[1] and , Families of exponentials : The method of moments in controllability problems for distributed paramenter systems. Cambridge University Press (1995). | MR | Zbl
[2] , and , Punctual control of a vibrating string : Numerical analysis. Comput. Maths. Appl. 4 (1978) 113-138. | MR | Zbl
[3] , Boundary controllability of the one-dimensional wave equation with rapidly oscillating density. Asymptotic Analysis 20 (1999) 317-350. | MR | Zbl
[4] and , Unique continuation and control for the heat equation from a lower dimensional manifold. SIAM J. Control. Optim. 42 (2005) 1400-1434. | MR | Zbl
[5] and , Wave propagation observation and control in 1-d flexible multi-structures. Math. Appl. 50 (2006). | Zbl
[6] and , Exact controllability and stabilization of a vibrating string with an interior point mass. SIAM J. Control Optim. 33 (1995) 1357-1391. | MR | Zbl
[7] , Controllability of the wave equation with moving point control. Appl. Math. Optim. 31 (1995) 155-175. | MR | Zbl
[8] , Mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation. SIAM J. Contol. Optim. 40 (2001) 231-252. | MR | Zbl
[9] , Observability and stabilization of the vibrating string equipped with bouncing point sensors and actuators. Math. Meth. Appl. Sci. 44 (2001) 1055-1072. | MR | Zbl
[10] and , Non-homogeneous boundary value problems and applications I. Springer-Verlag (1972). | MR | Zbl
[11] , Some methods in the mathematical analysis of systems and their control. Gordon and Breach (1981). | MR | Zbl
[12] , Contrôlabilité exacte, stabilisation et perturbations de systèmes distribués. RMA 8 and 9, Tomes 1 and 2, Masson, Paris (1988). | MR | Zbl
[13] , Pointwise control for distributed systems, in Control and estimation in distributed parameter systems, edited by H.T. Banks. SIAM (1992). | MR | Zbl
Cité par Sources :
