Free Access
Issue
ESAIM: COCV
Volume 19, Number 2, April-June 2013
Page(s) 317 - 336
DOI https://doi.org/10.1051/cocv/2012010
Published online 21 June 2012
  1. N.U. Ahmed, Finite-time null controllability for a class of linear evolution equations on a Banach space with control constraints. J. Optim. Theory Appl. 47 (1985) 129–158. [CrossRef] [Google Scholar]
  2. V. Barbu. Optimal control of variational inequalities. Res. Notes Math. 100 (1984). [Google Scholar]
  3. D. Barcenas, H. Leiva and T. Maya, The transversality condition for infinite dimensional control systems. Revista Notas de Matematica 4 (2008) 25–36. [Google Scholar]
  4. C. Bardos, G. Lebeau and J. Rauch, Un exemple d’utilisation des notions de propagation pour le contrôle et la stabilisation de problèmes hyperboliques, Nonlinear hyperbolic equations in applied sciences. Rend. Sem. Mat. Univ. Politec. Torino 1988 (1989) 11–31. [Google Scholar]
  5. H.O. Fattorini, The time optimal problem for distributed control of systems described by the wave equation, in Control theory of systems governed by partial differential equations (Conf. Naval Surface Weapons Center, Silver Spring, Md., 1976). Academic Press, New York (1977) 151–175. [Google Scholar]
  6. H.O. Fattorini, Infinite-dimensional optimization and control theory. Cambridge University Press, Cambridge. Encyclopedia of Mathematics and its Applications. 62 (1999). [Google Scholar]
  7. H.O. Fattorini, Infinite dimensional linear control systems, The time optimal and norm optimal problems. Elsevier Science B.V., Amsterdam. North-Holland Mathematics Studies. 201 (2005). [Google Scholar]
  8. M. Gugat, Penalty techniques for state constrained optimal control problems with the wave equation. SIAM J. Control Optim. 48 (2009/2010) 3026–3051. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Gugat and G. Leugering, L-norm minimal control of the wave equation : on the weakness of the bang-bang principle. ESAIM : COCV 14 (2008) 254–283. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  10. H. Hermes and J.P. LaSalle, Functional analysis and time optimal control. Academic Press, New York. Math. Sci. Eng. 56 (1969). [Google Scholar]
  11. K. Ito and K. Kunisch, Lagrange multiplier approach to variational problems and applications. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. Advances in Design and Control. 15 (2008). [Google Scholar]
  12. W. Krabs, On time-minimal distributed control of vibrating systems governed by an abstract wave equation. Appl. Math. Optim. 13 (1985) 137–149. [CrossRef] [MathSciNet] [Google Scholar]
  13. W. Krabs, On time-minimal distributed control of vibrations. Appl. Math. Optim. 19 (1989) 65–73. [CrossRef] [MathSciNet] [Google Scholar]
  14. I. Lasiecka, J.-L. Lions and R. Triggiani, Nonhomogeneous boundary value problems for second order hyperbolic operators. J. Math. Pures Appl. 65 (1986) 149–192. [Google Scholar]
  15. E.B. Lee and L. Markus, Foundations of optimal control theory. John Wiley & Sons Inc., New York (1967). [Google Scholar]
  16. J.-L. Lions, Exact controllability, stabilization and perturbations for distributed systems. SIAM Rev. 30 (1988) 1–68. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Peichl and W. Schappacher, Constrained controllability in Banach spaces. SIAM J. Control Optim. 24 (1986) 1261–1275. [CrossRef] [MathSciNet] [Google Scholar]
  18. K.D. Phung, G. Wang and X. Zhang, On the existence of time optimal controls for linear evolution equations. Discrete Contin. Dyn. Syst. Ser. B 8 (2007) 925–941. [CrossRef] [MathSciNet] [Google Scholar]
  19. E. Zuazua, Propagation, observation, and control of waves approximated by finite difference methods. SIAM Rev. 47 (2005) 197–243. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.