Free access
Issue
ESAIM: COCV
Volume 14, Number 2, April-June 2008
Page(s) 254 - 283
DOI http://dx.doi.org/10.1051/cocv:2007044
Published online 20 March 2008
  1. A. Barvinok, A course in convexity. AMS, Providence, Rhode Island (2002).
  2. J.K. Bennighof and R.L. Boucher, Exact minimum-time control of a distributed system using a traveling wave formulation. J. Optim. Theory Appl 73 (1992) 149–167. [CrossRef] [MathSciNet]
  3. F.H. Clarke, Optimization and Nonsmooth Analysis. John Wiley, New York (1983).
  4. A. Dovretzki, On Liapunov's convexity theorem. Proc. Natl. Acad. Sci 91 (1994) 2145. [CrossRef]
  5. V. Drobot, An infinte-dimensional version of Liapunov's convexity theorem. Michigan Math. J 17 (1970) 405–408. [CrossRef] [MathSciNet]
  6. C. Fabre, J.-P. Puel and E. Zuazua, Contrôlabilité approchée de l'équation de la chaleur linéaire avec des contrôles de norme Formula minimale. (Approximate controllability for the linear heat equation with controls of minimal Formula norm). C. R. Acad. Sci., Paris, Sér. I 316 (1993) 679–684.
  7. C. Fabre, J.-P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. R. Soc. Edinb., Sect. A 125 (1995) 31–61.
  8. M. Gugat, Time-parametric control: Uniform convergence of the optimal value functions of discretized problems. Contr. Cybern 28 (1999) 7–33.
  9. M. Gugat and G. Leugering, Regularization of Formula -optimal control problems for distributed parameter systems. Comput. Optim. Appl 22 (2002) 151–192. [CrossRef] [MathSciNet]
  10. M. Gugat, G. Leugering and G. Sklyar, lp-optimal boundary control for the wave equation. SIAM J. Control Optim 44 (2005) 49–74. [CrossRef] [MathSciNet]
  11. H. Hermes and J. Lasalle. Functional analysis and time optimal control. Academic Press (1969).
  12. T. Kato, Linear evolution equations of hyperbolic type. Univ. Tokyo Sec. I 17 (1970) 241–258.
  13. T. Kato, Perturbation theory for linear operators, Corr. printing of the 2nd edn. Springer (1980).
  14. W. Krabs, On moment theory and controllability of one-dimensional vibrating systems and heating processes, Lecture Notes in Control and Information Science 173. Springer-Verlag, Heidelberg (1992).
  15. W. Krabs, Optimal Control of Undamped Linear Vibrations. Heldermann Verlag, Lemgo, Germany (1995).
  16. C.M. Lee and F.D.K. Roberts, A comparison of algorithms for rational Formula approximation. Math. Comp 27 (1973) 111–121. [MathSciNet]
  17. E.B. Lee and L. Markus, Foundations of Optimal Control Theory. Wiley, New York (1968).
  18. J.-L. Lions, Exact controllability, stabilization and perturbations of distributed systems. SIAM Rev 30 (1988) 1–68. [CrossRef] [MathSciNet]
  19. A. Lyapunov, Sur les fonctions-vecteurs complètement additives. Bull. Acad. Sci. URSS, Sér. Math 4 (1940) 465–478.
  20. J. Macki and A. Strauss, Introduction to Optimal Control Theory. Springer-Verlag, New York (1982).
  21. V.J. Mizel and T.I. Seidman, An abstract bang-bang principle and time-optimal boundary control of the heat equation. SIAM J. Control Optim 35 (1997) 1204–1216. [CrossRef] [MathSciNet]
  22. N. Papageorgiu, Measurable multifunctions and their applications to convex integral functionals. Internat. J. Math. Math. Sciences 12 (1989) 175–192. [CrossRef]
  23. G.K. Pedersen, Analysis Now. Springer-Verlag, New York (1989).
  24. R.T. Rockafellar, Convex Analysis. Princeton University Press (1970).
  25. K. Yosida, Functional Analysis. Springer, Berlin (1965).
  26. E. Zuazua, Optimal and approximate control of finite-difference approximation schemes for the 1d wave equation. Rend. Mat. Appl 24 (2004) 201–237. [MathSciNet]
  27. E. Zuazua, Propagation, observation. and control of waves approximated by finite difference methods. SIAM Rev 47 (2005) 197–243. [CrossRef] [MathSciNet]
  28. E. Zuazua, Controllability of partial differential equations: Some results and open problems, in Handbook of Differential Equations: Evolutionary Differential Equations, C. Dafermos and E. Feireisl Eds., Elsevier Science (2006).