LPoptimal boundary control for the wave equation

SIAM Journal on Control and Optimization

Volumn 44, Issue 1, 2006, Pages 49-74

  Gugat, M ^a   Leugering, G ^a   Sklyar, G ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF SZCZECIN   (Poland)

Author keywords

Analytic solution; Boundary control; Controllability; Distributed parameter systems; Optimal control; Robust optimization; Sensitivity; State constraints; Test examples; Wave equation

Indexed keywords

BOUNDARY CONDITIONS; CONSTRAINT THEORY; OPTIMIZATION;

ANALYTIC SOLUTIONS; STATE CONSTRAINTS; TEST CONSTRAINTS;

WAVE EQUATIONS;

EID: 33144459259     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012903419212     Document Type: Article

References (21)

1. S. A. AVDONIN AND S. S. IVANOV, Families of Exponentials, Cambridge University Press, Cambridge, UK, 1995.
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), pp. 149-167.
3. J. F. BONNANS AND A. SHAPIRO, Perturbation Analysis of Optimization Problems, Springer New York, 2000.
4. A. G. BUTKOVSKI, The method of moments in optimal control theory with distributed parameter systems, Avtomat. i Telemeh., 24 (1963), pp. 1217-1225.
5. ∞ minimale, C.R. Acad. Sci. Paris, Sér. I Math., 316 (1993), pp. 679-684.
6. C. FABRE, J.-P. FUEL, AND E. ZUAZUA, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh Sect. A, 125 (1995), pp. 31-61.
7. R. GLOWINSKI AND J.-L. LIONS, Exact and approximate controllability for distributed parameter systems, Acta Numer., (1994), pp. 269-378.
8. R. GLOWINSKI AND J.-L. LIONS, Exact and approximate controllability for distributed parameter systems, Acta Numer., (1995), pp. 159-333.
9. R. GLOWINSKI, C. H. LI, AND J.-L. LIONS, A numerical approach to the exact boundary controllability of the wave equation. I. Dirichlet controls: Description of the numerical methods, Japan J. Appl. Math., 7 (1990), pp. 1-76.
10. ∞-optimal control problems for the wave equation, J. Optim. Theory Appl., 114 (2002), pp. 397-421.
11. ∞-optimal control problems for distributed parameter systems, Comput. Optim. Appl., 22 (2002), pp. 151-192.
12. p-norm-minimal control problems for the wave equation, Comput. Appl. Math., 21 (2002), pp. 227-244.
13. A. E. INGHAM, Some trigonometrical inequalities with applications to the theory of series, Math. Z., 41 (1936), pp. 367-379.
14. V. I. KOROBOV, W. KRABS, AND G. M. SKLYAR, Construction of the control realizing the rotation of a Timoshenko beam, J. Optim. Theory Appl., 107 (2000), pp. 51-68.
15. W. KRABS, Optimal Control of Undamped Linear Vibrations, Heldermann Verlag, Lemgo, 1995.
16. 1,p-controls for p ∈ [2, ∞], Math. Methods Appl. Sci., 17 (1994), pp. 77-93.
17. J. L. LIONS, Optimal Control of Systems Governed by Partial Differential Equations, Springer, Berlin, 1971.
18. S. MICU AND E. ZUAZUA, Boundary controllability of a linear hybrid systems arising in the control of noise, SIAM J. Control Optim., 35 (1997), pp. 1614-1637.
19. D. L. RUSSELL, Nonharmonic Fourier series in the control theory of distributed parameter systems, J. Math. Anal. Appl., 18 (1967), pp. 542-560.
20. E. ZUAZUA, Exact controllability for semilinear wave equations in one space dimension, Ann. Inst. H. Poincaré Anal. NonLinéaire, 10 (1993), pp. 109-129.
21. E. ZUAZUA, Optimal and approximate control of finite-difference approximation schemes for the 1D wave equation, Rend. Mat. Appl. (7), 24 (2004), pp. 201-237.