Necessary conditions for optimality in the identification of elliptic systems with parameter constraints

Journal of Optimization Theory and Applications

Volumn 88, Issue 3, 1996, Pages 725-742

  Yu, W H ^a  

^a TIANJIN UNIVERSITY   (China)

Author keywords

Distributed parameter systems; Maximum principle; One sided g teaux differentiable functionals; Parameter constraints; System identification

Indexed keywords

CONSTRAINT THEORY; PARAMETER ESTIMATION;

CONDITION FOR OPTIMALITY; DISTRIBUTED PARAMETER SYSTEMS; ELLIPTIC SYSTEM; EQUALITY CONSTRAINTS; FUNCTIONALS; MEASUREMENT DATA; ONE-SIDED GÂTEAUX DIFFERENTIABLE FUNCTIONALS; PARAMETER CONSTRAINTS; SYSTEM-IDENTIFICATION; UNIFORMLY ELLIPTIC EQUATIONS;

MAXIMUM PRINCIPLE;

EID: 0030542762     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02192207     Document Type: Article

References (27)

1. ANIKONOV, YU. E., Generating Functions, Evolution Equations, and Inverse Problems, Doklady Akademii Nauk, Vol. 323, pp. 172-174, 1992 (In Russian).
2. BANKS, H. T., and KUNISCH, K., Estimation Techniques for Distributed-Parameter Systems, Birkhäuser, Boston, Massachusetts, 1989.
3. BANKS, H. T., REICH, S., and ROSEN, I. G., An Approximation Theory for the Identification of Nonlinear Distributed-Parameter Systems, SIAM Journal on Control and Optimization, Vol. 28, pp. 523-569, 1990.
4. BARBU, V., The Approximate Solvability of the Inverse One-Phase Stefan Problem, International Series of Numerical Mathematics, Vol. 99, pp. 33-43, 1991.
5. BELOV, YU. YA., On an Inverse Problem for a Semilinear Parabolic Equation, Soviet Mathematics Doklady, Vol. 43, pp. 216-220, 1991.
6. CANNON, J. R., and RUNDELL, W., An Inverse Problem for an Elliptic Partial Differential Equation, Journal of Mathematical Analysis and Applications, Vol. 126, pp. 329-340, 1987.
7. CHAVENT, G., Identification of Distributed-Parameter Systems: About the Output Least-Square Method, Its Implementation, and Identifiability, Identification and System Parameter Estimation, Edited by R. Isermann, Pergamon, New York, New York, pp. 85-97, 1982.
8. CHEN, Y. M., and ZHANG, F. G., Hierarchical Multigrid Strategy for Efficiency Improvement of the GPST Inversion Algorithm, Applied Numerical Mathematics, Vol. 6, pp. 431-446, 1990.
9. FRIEDMAN, A., and GUSTAFSSON, B., Identification of the Conductivity Coefficient in an Elliptic Equation, SIAM Journal on Mathematical Analysis, Vol. 18, pp. 777-787, 1987.
10. GUYON, F., and YVON, J. P., On a Weighing Method Improving the Identifiability of Distributed-Parameter Systems, Lecture Notes in Control and Information Sciences, Springer Verlag, Berlin, Germany, Vol. 149, pp. 104-119, 1991.
11. HU, S. J., and YU, W. H., Identification of the Surface Temperature in a Floated Gyroscope, Proceedings of the 3rd IFAC Symposium of Control of Distributed-Parameter Systems, Toulouse, France, pp. 347-352, 1982.
12. ISAKOV, V., Inverse Source Problems, American Mathematical Society, Providence, Rhode Island, 1990.
13. KORN, R. V., and VOGELIUS, M., Determining Conductivity by Boundary Measurements, Communications on Pure and Applied Mathematics, Vol. 37, pp. 289-298, 1984.
14. LAVRENT'EV, M. M., ROMANOV, V. G., and SHISHATSKII, X. X., Ill-Posed Problems of Mathematical Physics and Analysis, Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, Vol. 64, 1986.
15. ROMANOV, V. G., Inverse Problems of Mathematical Physics, VNU Science Press BV, Utrecht, Netherlands, 1987.
16. SUZUKI, T., Gelfand-Levitan Theory and Related Inverse Problems, Inverse Problems: Proceedings of a Conference Held at the Mathematical Research Institute, Oberwolfach, Germany, 1986; Edited by J. R. Cannon and U. Hornung, Birkhäuser Verlag, Basel, Switzerland, pp. 163-171, 1986.
17. SYLVESTER, J., and UHLMANN, G., Inverse Boundary-Value Problems at the Boundary-Continuous Dependence, Communications of Pure and Applied Mathematics, Vol. 41, pp. 197-219, 1988.
18. YU, W. H., On Well-Posedness of Inverse Problems for a Class of Hyperbolic Equations, Chinese Mathematical Annals, Vol. 10, pp. 1-9, 1988.
19. YU, W. H., A Rapid Convergent Iteration Method for Identifying Distributed Parameters in Partial Differential Equations, IFAC Symposium on Identification and System Parameter Estimation, Beijing, China, 1988.
20. YU, W. H., and SEINFELD, J. H., Identification of Parabolic Distributed-Parameter Systems by Regularization with Differential Operators, Journal of Mathematical Analysis and Applications, Vol. 132, pp. 365-398, 1988.
21. YU, W. H., and SEINFELD, J. H., Identification of Distributed-Parameter Systems with Pointwise Constraints on the Parameters, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 497-520, 1988.
22. GILGARG, D., and TRUDINGER, N. S., Elliptic Partial Differential Equations of Second Order, Springer Verlag, New York, New York, 1977.
23. GIRSANOV, I. V., Lectures on the Mathematical Theory of Extremum Problems, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 67, 1972.
24. ZEIDLER, E., Nonlinear Functional Analysis and Its Applications, Vol. 3: Variational Methods and Optimization, Springer Verlag, Berlin, Germany, 1985.
25. DUNFORD, N., and SCHWARTZ, J. T., Linear Operators, Vol. 1, Interscience Publishers, New York, New York, 1958.
26. LUSTERNIK, L. A., and SOBOLEV, V. J., Elements of Functional Analysis, Hindustan Publishing Corporation, Delhi, India, 1961.
27. LIONS, J. L., and MAGENES, E., Nonhomogeneous Boundary-Value Problems and Applications, Vols. 1-2, Springer Verlag, New York, New York, 1972.