Simultaneous controllability in sharp time for two elastic strings

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 6, Issue , 2001, Pages 259-273

  Avdonin, Sergei ^a,b   Tucsnak, Marius ^c  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b FLINDERS UNIVERSITY   (Australia)

^c UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Approximate controllability; Boundary control; Exact controllability; Riesz basis; Simultaneous controllability; Spectral controllability; String equation

Indexed keywords

APPROXIMATION THEORY; CONTROLLABILITY; MATHEMATICAL MODELS; STATE SPACE METHODS;

APPROXIMATE CONTROLLABILITY; ELASTIC STRINGS; EXACT CONTROLLABILITY; SIMULTANEOUS CONTROLLABILITY; SPECTRAL CONTROLLABILITY;

CONTROL SYSTEM ANALYSIS;

EID: 0035693708     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2001110     Document Type: Article

References (19)

1. S.A. Avdonin, Simultaneous controllability of several elastic strings, in Proc. CD of the Fourteenth International Symposium on Mathematical Theory of Networks and Systems. Perpignan, France, June 19-23 (2000).
2. S.A. Avdonin and S.A. Ivanov, Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems. Cambridge University Press, New York (1995).
3. C. Baiocchi, V. Komornik and P. Loreti, Ingham type theorems and applications to control theory. Boll. Un. Mat. Ital. B 2 (1999) 33-63.
4. C. Baiocchi, V. Komornik and P. Loreti, Generalisation d’un theorème de Beurling et application à la theorie du contrôle. C. R. Acad. Sci. Paris Sér. I Math. 330 (2000) 281-286.
5. J.W.S. Cassels, An Introduction to Diophantine Approximation. Cambridge University Press, Cambridge (1965).
6. S. Dolecki and D.L. Russell, A general theory of observation and control. SIAM J. Control Optim. 15 (1977) 185-220.
7. S. Jaffard, M. Tucsnak and E. Zuazua, Singular internal stabilization of the wave equation. J. Differential Equations 145 (1998) 184-215.
8. S. Jaffard, M. Tucsnak and E. Zuazua, On a theorem of Ingham. J. Fourier Anal. Appl. 3 (1997) 577-582.
9. L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences. John Wiley &Sons, New York (1974).
10. J.E. Lagnese and J.L. Lions, Modelling, Analysis and Control of Thin Plates. Masson, Paris (1988).
11. S. Lang, Introduction to Diophantine Approximations. Addison Wesley, New York (1966).
12. J.-L. Lions, Controlabilité Exacte Perturbations et Stabilisation de Systèmes Distribués, Volume 1. Masson, Paris (1988).
13. N.K. Nikol’skii, A Treatise on the Shift Operator. Moscow, Nauka, 1980 (Russian); Engl. Transl., Springer, Berlin (1986).
14. B.S. Pavlov, Basicity of an exponential systems and Muckenhoupt’s condition. Dokl. Akad. Nauk SSSR 247 (1979) 37-40 (Russian);
15. B.S. Pavlov, English transl. in Soviet Math. Dokl. 20 (1979) 655-659.
16. W. Rudin, Real and complex analysis. McGraw-Hill, New York (1987).
17. D.L. Russell, The Dirichlet-Neumann boundary control problem associated with Maxwell’s equations in a cylindrical region. SIAM J. Control Optim. 24 (1986) 199-229.
18. M. Tucsnak and G. Weiss, Simultaneous exact controllability and some applications. SIAM J. Control Optim. 38 (2000) 1408-1427.
19. R. Young, An Introduction to Nonharmonic Fourier Series. Academic Press, New York (1980).