Geodesic
Reconstruction of controls and parameters by the Tikhonov method with non-smooth stabilizers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2009), pp. 76-82.

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We consider the problem of the reconstruction of an a priori unknown control in a dynamic system based on approximate a posteriori observations of the motion of this system. We propose to solve this problem by the Tikhonov method with a stabilizer which contains the total variation of the control. This provides the piecewise uniform convergence of regularized approximations and thus enables one to numerically reconstruct the fine structure of the desired solution.
Keywords: controlled system, inverse problem of dynamics, Tikhonov regularization method, subgradient.
Mots-clés : total variation, piecewise uniform convergence 
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     title = {Reconstruction of controls and parameters by the {Tikhonov} method with non-smooth stabilizers},
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M. A. Korotkii. Reconstruction of controls and parameters by the Tikhonov method with non-smooth stabilizers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2009), pp. 76-82. http://geodesic.mathdoc.fr/item/IVM_2009_2_a5/

[1] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979, 288 pp.

[2] Ivanov V. K., Vasin V. V., Tanana V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978, 206 pp. | MR

[3] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Nauka, M., 1976, 392 pp. | MR | Zbl

[4] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[5] Osipov Yu. S., Kryazhimskii A. V., Inverse problems of ordinary differential equations: dynamical solutions, Gordon and Breach, London, 1995, 625 pp. | MR | Zbl

[6] Ageev A. L., “Regulyarizatsiya nelineinykh operatornykh uravnenii na klasse razryvnykh funktsii”, Zhurn. vychisl. matem. i matem. fiz., 20:4 (1980), 819–836 | MR

[7] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002, 824 pp.

[8] Polyak B. T., Vvedenie v optimizatsiyu, Nauka, M., 1983, 384 pp. | MR

[9] Vasin V. V., Korotkii M. A., “Tikhonov regularization with nondifferentiable stabilizing functional”, J. Inverse and Ill-Posed Problems, 15:8 (2007), 853–865 | DOI | MR | Zbl