On one algorithm for solving the problem of source function reconstruction

• Autorzy: Vyacheslav Maksimov
• Języki publikacji: EN

Abstrakty

EN

In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the sum of a quality criterion and a linear penalty term is minimized. This procedure is robust to perturbations in problems data.

Słowa kluczowe

EN

reconstruction; source function; feedback control

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2010
• Tom: 20
• Numer: 2
• Strony: 239-247

Daty

wydano

2010

otrzymano

2009-09-14

poprawiono

2010-01-19

Twórcy

autor

Vyacheslav Maksimov

• Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskoi Str., Ekaterinburg, 620219 Russia

Bibliografia

• Bensoussan, A., Prato, G.D., Delfour, M. and Mitter, S. (1992). Representation and Control of Infinite Dimensional Systems, Vol. I, Birkhäuser, Boston, MA.
• Blizorukova, M.S. and Maksimov, V. I. (1998). On the reconstruction of an extremal input in a system with hereditary, Vestnik PGTU. Matematika i Prikladnaya Matematika (Mathematics and Applied Mathematics) 4(4): 51-61, (in Russian).
• Digas, B.V., Maksimov, V.I., Lander, A.V. and Bukchin, B.G. (2003). On an algorithm for solving the inverse problem of ray seismics, in D. Chowdhury (Ed.), Computational Seismology and Geodynamics, American Geophysical Union, Washington, DC, pp. 84-92.
• Korbicz, J. and Zgurowski, M. (1991). Estimation and Control of Stochastic Distributed-Parameter Systems, Polish Scientific Publishers, Warsaw, (in Polish).
• Krasovskii, N. and Subbotin, A. (1988). Game-Theoretical Control Problems, Springer, Berlin.
• Kryazhimskii, A.V., Maksimov, V.I. and Osipov, Yu.S. (1997). Reconstruction of extremal disturbances in parabolic equations, Journal of Computational Mathematics and Mathematical Physics 37(3): 119-125, (in Russian).
• Kryazhimskii, A.V. and Osipov, Yu.S. (1987). To a regularization of a convex extremal problem with inaccurately given constraints. An application to an optimal control problem with state constraints, in A.I. Korotkii and V.I. Maksimov (Eds.), Some Methods of Positional and Program Control, Ural Scientific Center, Sverdlovsk, pp. 34-54, (in Russian).
• Omatu, S. and Seinfeld, J. (1989). Distributed Parameter Systems: Theory and Applications, Oxford Mathematical Monographs, Oxford University Press, New York, NY.
• Uciński, D. (1999). Measurement Optimization for Parameter Estimation in Distributed Systems, Technical University Press, Zielona Góra.
• Vasiliev, F. (1981). Solution Methods to Extremal Problems, Nauka, Moscow, (in Russian).

Identyfikatory

DOI

10.2478/v10006-010-0017-3