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Global stabilization of a coupled system of two generalized Korteweg-de Vries type equations posed on a finite domain
Coefficient identification and fault detection in linear elastic systems; one dimensional problems
1. | Department of Mathematics, 460 McBryde Hall, Virginia Tech, Blacksburg, VA 24060, United States |
References:
[1] |
A. I. Artjukh and N. V. Banichuk, Application of optimization methods to identification problems, in "Proceedings of the Workshop on Optimization and Optimal Control" (Jyväskylä, 1992), Report 58, Univ. Jyväskylä, Jyväskylä, (1993), 5-16. |
[2] |
N. V. Banichuk, Optimization formulation and decomposition of the problem of the identification of the distributed parameters of elastic constructions, (Russian) Dokl. Akad. Nauk, 367 (1999), 48-51; translation in Dokl. Phys., 44 (1999), 446-449. |
[3] |
H. T. Banks and K. Kunisch, "Estimation Techniques for Distributed Parameter Systems," Syst. & Contr: Found. and Appl., 1, Birkhäuser Boston, Inc., Boston, MA, 1989. |
[4] |
H. T. Banks, R. H. Fabiano and K. Ito, eds., "Identification and Control in Systems Governed by Partial Differential Equations," Proc. AMS-IMS-SIAM Joint Sumr. Res. Conf. on Control and Identification of Partial Differential Equations, Mt. Holyoke College, South Hadley, MA, July 1992, Society for Industrial and Applied Mathematics, Philadelphia, 1993. |
[5] |
T. Feng, N. Yan and W. Liu, Adaptive finite element methods for the identification of distributed parameters in elliptic equation, Adv. Comput. Math., 29 (2008), 27-53.
doi: 10.1007/s10444-007-9035-6. |
[6] |
P. R. Gill, W. Murray and M. H. Wright, The Levenberg-Marquardt Method, S 4.7.3, in "Practical Optimization," Academic Press, London, 1981, 136-137. |
[7] |
T. T. Marinov, R. S. Marinova and C. I. Christov, Coefficient identification in elliptic partial differential equation, in "Large-scale Scientific Computing," Lecture Notes in Comput. Sci., 3743, Springer, Berlin, 2006, 372-379. |
[8] |
Z. Mróz and G. E. Stavroulakis, "Parameter Identification of Materials and Structures," Springer Verlag, Vienna, New York, 2005. |
[9] |
D. L. Russell, Structural parameter optimization in linear elastic systems, Commun. Pure & Appl. Anal., 10 (2011), 1517-1536. |
[10] |
D. L. Russell, Gauss-Newton and inverse Gauss-Newton methods for coefficient identification in linear elastic systems, to appear in Acta Applicandae Mathematicae. |
[11] |
D. L. Russell, Some methods for parameter identification in Elliptic Systems, to appear. |
[12] |
J. Schoukens and R. Pintelon, "Identification of Linear Systems. A Practical Guideline to Accurate Modeling," Pergamon Press, Oxford, 1991. |
[13] |
U. Tautenhahn, A fast iterative method for solving regularized parameter identification problems in elliptic boundary value problem, Computing, 43 (1989), 47-58.
doi: 10.1007/BF02243805. |
show all references
References:
[1] |
A. I. Artjukh and N. V. Banichuk, Application of optimization methods to identification problems, in "Proceedings of the Workshop on Optimization and Optimal Control" (Jyväskylä, 1992), Report 58, Univ. Jyväskylä, Jyväskylä, (1993), 5-16. |
[2] |
N. V. Banichuk, Optimization formulation and decomposition of the problem of the identification of the distributed parameters of elastic constructions, (Russian) Dokl. Akad. Nauk, 367 (1999), 48-51; translation in Dokl. Phys., 44 (1999), 446-449. |
[3] |
H. T. Banks and K. Kunisch, "Estimation Techniques for Distributed Parameter Systems," Syst. & Contr: Found. and Appl., 1, Birkhäuser Boston, Inc., Boston, MA, 1989. |
[4] |
H. T. Banks, R. H. Fabiano and K. Ito, eds., "Identification and Control in Systems Governed by Partial Differential Equations," Proc. AMS-IMS-SIAM Joint Sumr. Res. Conf. on Control and Identification of Partial Differential Equations, Mt. Holyoke College, South Hadley, MA, July 1992, Society for Industrial and Applied Mathematics, Philadelphia, 1993. |
[5] |
T. Feng, N. Yan and W. Liu, Adaptive finite element methods for the identification of distributed parameters in elliptic equation, Adv. Comput. Math., 29 (2008), 27-53.
doi: 10.1007/s10444-007-9035-6. |
[6] |
P. R. Gill, W. Murray and M. H. Wright, The Levenberg-Marquardt Method, S 4.7.3, in "Practical Optimization," Academic Press, London, 1981, 136-137. |
[7] |
T. T. Marinov, R. S. Marinova and C. I. Christov, Coefficient identification in elliptic partial differential equation, in "Large-scale Scientific Computing," Lecture Notes in Comput. Sci., 3743, Springer, Berlin, 2006, 372-379. |
[8] |
Z. Mróz and G. E. Stavroulakis, "Parameter Identification of Materials and Structures," Springer Verlag, Vienna, New York, 2005. |
[9] |
D. L. Russell, Structural parameter optimization in linear elastic systems, Commun. Pure & Appl. Anal., 10 (2011), 1517-1536. |
[10] |
D. L. Russell, Gauss-Newton and inverse Gauss-Newton methods for coefficient identification in linear elastic systems, to appear in Acta Applicandae Mathematicae. |
[11] |
D. L. Russell, Some methods for parameter identification in Elliptic Systems, to appear. |
[12] |
J. Schoukens and R. Pintelon, "Identification of Linear Systems. A Practical Guideline to Accurate Modeling," Pergamon Press, Oxford, 1991. |
[13] |
U. Tautenhahn, A fast iterative method for solving regularized parameter identification problems in elliptic boundary value problem, Computing, 43 (1989), 47-58.
doi: 10.1007/BF02243805. |
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