Local controllability of a one-dimensional beam equation

SIAM Journal on Control and Optimization

Volumn 47, Issue 3, 2008, Pages 1219-1273

  Beauchard, Karine ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Beam equation; Bilinear control problem; Control of partial differential equations; Nash Moser theorem; Trigonometric moment problem

Indexed keywords

CIRCUIT THEORY; CONTROL THEORY; CONTROLLABILITY;

BEAM EQUATION; BEAM EQUATIONS; BILINEAR CONTROL PROBLEM; CLAMPED ENDS; CONTROL FUNCTIONS; FUNCTIONAL SPACES; LOCAL CONTROLLABILITIES; MOMENT THEORIES; MOSER THEOREMS; NASH-MOSER THEOREM; TRIGONOMETRIC MOMENT PROBLEM;

PROBABILITY DENSITY FUNCTION;

EID: 55549119623     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/050642034     Document Type: Article

References (22)

1. J. M. BALL, J. E. MARSDEN, AND M. SLEMROD, Controllability for distributed bilinear systems, SIAM J. Control Optim., 20 (1982), pp. 575-597.
2. K. BEAUCHARD, Controllability of a quantum particle in a 1D variable domain, ESAIM Control Optim. Calc. Var., 14 (2008), pp. 105-147.
3. K. BEAUCHARD, Local controllability of a 1D Schrödinger equation, J. Math. Pures Appl., 9 (2005), pp. 851-956.
4. K. BEAUOHARD AND J.-M. CORON, Controllability of a quantum particle in a moving potential well, J. Funct. Anal., 232 (2006), pp. 328-389.
5. J.-M. CORON, Global asymptotic stabilization for controllable systems without drift, Math. Control Signals Systems, 5 (1992), pp. 295-312.
6. J.-M. CORON, Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris, 317 (1993), pp. 271-276.
7. J.-M. CORON, On the controllability of the 2-D incompressible perfect fluids, J. Math. Pures Appli., 75 (1996), pp. 155-188.
8. J.-M. CORON, Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, ESAIM Control Optim. Calc. Var., 8 (2002), pp. 513-554.
9. J.-M. CORON AND A. FURSIKOV, Global exact controllability of the 2D Navier-Stokes equations on a manifold without boundary, Russian J. Math. Phys., 4 (1996), pp. 429-448.
10. J.-M. CORON, Control and nonlinearity, Math. Surveys Monogr., 136 (2007), 427 pp.
11. A. V. FURSIKOV AND O. YU. EMANUILOV, Exact controllability of the Navier-Stokes and Boussinesq equations, Uspekhi Mat. Nauk, 54 (1999), pp. 93-146 (in Russian); Russian Math. Surveys, 54 (1999), pp. 565-618 (in English).
12. O. GLASS, Exact boundary controllability of 3D-Euler equation, ESAIM Control Optim. Calc. Var., 5 (2000), pp. 1-44.
13. O. GLASS, An addendum to a J.-M. Coron theorem concerning the controllability of the Euler system for 2D incompressible inviscid fluids, J. Math. Pures Appl., 80 (2001), pp. 845-877.
14. O. GLASS, On the controllability of the Vlasov Poisson system, J. Differential Equations, 195 (2003), pp. 332-379.
15. O. GLASS, Asymptotic stabilizability by stationary feedback of the two-dimensional Euler equation: The multiconnected case, SIAM J. Control Optim., 44 (2005), pp. 1105-1147.
16. O. GLASS, Controllability and Asymptotic Stabilization of the Camassa-Holm Equation, preprint, 2007.
17. O. GLASS, On the controllability of the 1-D isentropic Euler equation, J. Eur. Math. Soc. (JEMS), 9 (2007), pp. 427-486.
18. O. GLASS AND S. GUERRERO, On the uniform controllability of the Burgers equation, SIAM J. Control Optim., 46 (2007), pp. 1211-1238.
19. M. GROMOV, Partial Differential Relations, Springer-Verlag, Berlin, 1986.
20. L. HÖRMANDER, On the Nash-Moser implicit function theorem, Ann. Acad. Sci. Fenn. Ser. A I Math., 10 (1985), pp. 255-259.
21. T. HORSIN, On the controllability of the Burgers equation, ESAIM Control Optim. Calc. Var., 3 (1998), pp. 83-95.
22. W. KRABS, On Moment Theory and Controllability of One-Dimensional Vibrating Systems and Heating Processes, Springer-Verlag, Berlin, 1992.