Source identification for parabolic equations

Mathematics of Control, Signals, and Systems

Volumn 16, Issue 2-3, 2003, Pages 141-157

  Sivergina, Irina F ^a,b   Polis, Michael P ^a   Kolmanovsky, Ilya ^c  

^a OAKLAND UNIVERSITY   (United States)

^b INSTITUTE OF MATHEMATICS AND MECHANICS   (Russian Federation)

^c FORD MOTOR COMPANY   (United States)

Author keywords

Identification; Parabolic system; Pollution control; Recursive estimation; Regularization; Sensor

Indexed keywords

ALGORITHMS; ESTIMATION; INVERSE PROBLEMS; MATHEMATICAL MODELS; POLLUTION CONTROL;

PARABOLIC EQUATION; RECURSIVE ESTIMATION ALGORITHM; REGULARIZATION; SOURCE IDENTIFICATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0142216422     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00498-003-0136-6     Document Type: Article

References (25)

1. Alpay ME, Shor MH (2000) Model-based solution techniques for the source localization problem, IEEE Trans. Control Systems Technol., 8:895-904
2. Alt HW, Hoffmann KH, Sprekels J (1984) A numerical procedure to solve certain identification problems, Internat. Ser. Numer. Math., 68:11-43
3. Banks HT, Kunish K (1989) Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, MA
4. Bartolini G, Ferrara A, Stotsky A (1999) Robustness and performance of an indirect adaptive control scheme in presence of bounded disturbances, IEEE Trans. Automat. Control, 44:789-793
5. Curtain RF, Pritchard AJ (1978) Infinite Dimensional Linear System Theory, Springer-Verlag, Berlin
6. Dunford N, Schwartz J (1958) Linear Operators, Vols. I and II, Interscience, New York
7. Hettlich F, Rundell W (2001) Identification of a discontinuous source in the heat equation, Inverse Problems, 17:1465-1482
8. Ioannou PA, Sun J (1996) Robust Adaptive Control, Prentice-Hall, London
9. Ivanov VK, Vasin VV, Tanana VP (1978) Theory of Linear Ill-Posed Problems and Its Applications (Russian), Nauka, Moscow
10. Kolmanovsky I, Siverguina I (2001) Adaptive identification schemes in presence of bounded disturbances: an automotive case study, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, 3-7 December 508-513
11. Kravoskii NN, Subbotin AI (1988) Game-Theoretical Control Problems, Springer-Verlag, New York
12. Kryazhimskii AV, Maksimov VI, Osipov YS (1997) On the reconstruction of extreme perturbations in parabolic systems, Comput. Math. Math. Phys., 37:288-298
13. Kurzhanskii AB, Khapalov AY (1991) An observation theory for distributed-parameter systems, Math. System. Estim. Control, 1:389-440
14. Kurzhanskii AB, Sivergina IF (1998) Dynamic programming in problems of the identification of systems with distributed parameters, J. Appl. Math. Mech., 62:831-842
15. Ladyzenskaja OA, Solonnikov VA, Ural'ceva NN (1968) Linear and Quasi-Linear Equations of Parabolic Type, American Mathematical Society, Providence, RJ
16. Lions J-L, Magenes E (1968) Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris
17. Marchuk GI (1986) Mathematical Models in Environmental Problems, Studies in Mathematics and its Applications, Vol. 16, North-Holland, Amsterdam
18. Omatu S, Seinfeld JH, Sawaragi J (1988) Estimation of nitrogen dioxide concentrations in the vicinity of a roadway by optimal filtering theory, Automatica, 24:19-29
19. Orlov Y, Bentsman J (2000) Adaptive distributed parameter systems identification with enforceable identifiability conditions and reduced-order spatial differentiation, IEEE Trans. Automat. Control, 45:203-216
20. Rozenberg VL (1995) On the problem of dynamic reconstruction of a source function in a parabolic equation (Russia), Proceedings of the Institute of Mathematics and Mechanics, Vol. 3, Ross. Akad. Nauk, Ural Otdel., Inst., Mat. Mekh., Ekaterinburg, pp. 183-201
21. Sakawa Y (1975) Observability and related problems for partial differential equations of parabolic type, SIAM J. Control, 13:14-27
22. Seinfeld JH (1998) Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, Wiley, New York
23. Sivergina IF (1996) Invertibility and observability of evolution systems, Dokl. Akad. Nauk, 351:304-308
24. Sivergina IF, Polis MP (2002) Comments on "Model-based solution techniques for the source localization problem", IEEE Trans. Control System Technol., 10:633
25. Tikhonov AN, Arsenin VY (1977) Solutions of Ill-Posed Problems, Winston, Washington