 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ĎĚĚ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| M.A. Korotkii, "The reconstruction of controls by regularization methods with uneven stabilizers," J. Appl. Math. Mech. 73 (1), 26-35 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
26-35 |
| Title |
The reconstruction of controls by regularization methods with uneven stabilizers |
| Author(s) |
M.A. Korotkii (Ekaterinburg, Russia, m_korotkii@list.ru) |
| Abstract |
The problem of reconstructing a previously unknown control (parameter) of a dynamical system using the results of approximate observations of the motion of this system is considered. It is proposed to use static and dynamic methods to solve this problem which, in their implementation, utilize the method of Tikhonov regularization with a stabilizer containing a variation of the simulating subsidiary control (parameter).The use of such a non-differentiable stabilizer enables one to obtain more refined results than the approximation of the required control in Lebesgue spaces. In particular, the piecewise-uniform convergence of the regularized approximations can be successfully substantiated by this route, which opens up the possibility of numerically reconstructing the fine structure of the required control. |
| References |
| 1. | A.N. Tikhonov and B.Y. Arsenin, Solutions of Ill-Posed Problems, Wiley, New York (1977). |
| 2. | V.K. Ivanov, V.V. Vasin and V.P. Tanana, Theory of Linear Ill-Posed Problems and its Applications, VSP, Utrecht (2002). |
| 3. | M.M. Lavrent’ev, V.G. Romanov and S.P. Shishatskii, Ill-Posed Problems of Mathematical Physics and Analysis, AMS, Providence RI (1980). |
| 4. | L.S. Pontryagin, V.G. Boltyansky, R.V. Gamkrelidze and E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York (1962). |
| 5. | N.N. Krasovskii and A.I. Subbotin, Positional Differential Games, Springer, New York (1988). |
| 6. | A.V. Kryazhimskii and Yu.S. Ospipov, The modelling of a control in a dynamical system, Izv Akad Nauk SSSR Tekhn Kibernetika 2 (1983), pp. 51–60. |
| 7. | Yu.S. Osipov and A.V. Kryazhimskii, Inverse Problems of Ordinary Differential Equations: Dynamical Solutions, Gordon & Breach, London (1995) 625p.. |
| 8. | Yu.S. Osipov, F.P. Vasil’ev and M.M. Potapov, Principles of the Method of Dynamic Regularization, Izd MGU, Moscow (1999). |
| 9. | V.I. Maksimov, Problems of the Dynamic Reconstruction of the Inputs of Infinite-Dimensional Systems, UrO Ross Akad Nauk, Ekaterinburg (2000). |
| 10. | A.B. Kurzhanskii, Control and Observation under Uncertainty Conditions, Nauka, Moscow (1977). |
| 11. | F.L. Chernous’ko and A.A. Melikyan, Game Problems of Control and Search, Nauka, Moscow (1978). |
| 12. | J. Warge, Optimal Control of Differential and Functional Equations, Acad Press, New York (1972). |
| 13. | P.D. Krut’ko, Inverse Problems in the Dynamics of Control Systems. Non-Linear Models, Nauka, Moscow (1988). |
| 14. | A.L. Ageyev, Regularization of non-linear operator equations in a class of continuous functions, Zh Vychisl Mat Mat Fiz 20 (4) (1980), pp. 819–826. |
| 15. | V.V. Vasin, Stable approximation of the nonsmooth solutions of ill-posed problems, Dokl Ross Akad Nauk 402 (5) (2005), pp. 586–589. |
| 16. | V.V. Vasin, Approximation of the nonsmooth solutions of linear ill-posed problems, Tr Inst Mat Mekh UrO Ross Akad Nauk 12 (1) (2006), pp. 64–77. |
| 17. | V.V. Vasin and M.A. Korotkii, Tikhonov regularization with nondifferentiable stabilizing functional, J Inv Ill-Posed Problems 15 (8) (2007), pp. 853–865. |
| 18. | A.S. Leonov, Regularization of ill-posed problems in Sobolev space W1, J Inv Ill-Posed Problems 13 (6) (2005), pp. 595–619. |
| 19. | A.S. Leonov, Piecewise-uniform regularization of ill-posed problems with discontinuous solutions, Zh Vychisl Mat Mat Fiz 22 (3) (1982), pp. 516–531. |
| 20. | A.N. Tikhonov, A.S. Leonov and A.G. Yagola, Non-Linear Ill-Posed Problems Vols 1 and 2, Chapman & Hall, London (1998). |
| 21. | E. Giusti, Minimal Surfaces and Functions of Bounded Variations, Birkhauser, Basel (1984) 239p. |
| 22. | R. Acar and C.R. Vogel, Analysis of bounded variation penalty method for ill-posed problems, Inverse Problems 10 (6) (1994), pp. 1217–1229. |
| 23. | G. Chavent and K. Kunish, Regularization of linear lease squares problems by total bounded variation, Control, Optimization, and Calculus of Variation 2 (1997), pp. 359–376. |
| 24. | C.R. Vogel, Computation Methods for Inverse Problems, SIAM, Philadelphia (2002) 183p. |
| 25. | A.N. Kolmogorov and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York (1989). |
| 26. | K. Yosida, Functional Analysis, Springer, Berlin (1966). |
| 27. | F.P. Vasil’ev, Optimization Methods, Factorial, Moscow (2002). |
| 28. | A.D. Ioffe and V.M. Tikhomirov, Theory of Extremal Problems, North-Holland, Amsterdam (1979). |
| 29. | B.T. Polyak, Introduction to Optimization, Optimization Software Inc Public Div, New York (1987). |
|
| Received |
20 May 2008 |
| Link to Fulltext |
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