Inverse Problems for Dynamic Systems: Classification and Solution Methods

Menshikov Yu^{*}

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References

[1] L. P. Lebedev, I. I. Vorovich and G. M. Gladwell, “Functional Analysis: Applications in Mechanics and Inverse Problems (Solid Mechanics and Its Applications),” Springer, Berlin, 2002.

[2] G. M. L. G. Gladwell, “Inverse Problems in Vibration,” PDF Kluwer Academic Publishers, New York, 2005.

[3] K. P. Gaikovich, “Inverse Problems in Physical Diagnostics,” Longman Scientific & Technical, Harlow, 1988.

[4] Yu. L. Menshikov, “Adequate Mathematical Description of Dynamic System: Statement Problem, Synthesis Methods,” Proceedings of the 7th EUROSIM Congress on Modelling and Simulation, Vol. 2, 2010, 7 p.

[5] Yu. L. Menshikov, “Synthesis of Adequate Mathematical Description as Inverse Problem,” Proceedings of 5th International Conference on Inverse Problems: Modeling & Simulation, Antalya, 24-29 May 2010, pp. 185-186.

[6] Proceedings of International Conference, “Identification of Dynamical Systems and Inverse Problems,” MAI, Moscow, 1994.

[7] Yu. L. Menshikov, “The Inverse Krylov Problem,” Computational Mathematics and Mathematical Physics, Vol. 43, No. 5, 2003, pp. 633-640.

[8] W. Q. Yang and L. H. Peng, “Image Reconstruction Algorithms for Electrical Capacitance Tomography,” Journal of Measurement Science and Technology, Vol. 14, No. 1, pp. 123-134.

[9] Fr. Zirilli, “Inverse Problems in Mathematical Finance,” Proceedings of 5th International Conference on Inverse Problems: Modeling & Simulation, Turkey, 24-29 May 2009, pp. 185-186.

[10] Yu. L. Menshikov and G. I. Yach, “Identification of Moment of Technological Resistance on Rolling Mill of Sheets,” Proceedings of Higher Institutes. Ferrous Metallurgy, Moscow, No. 9, 1977, pp. 69-73.

[11] Yu. L. Menshikov, “Identification of External Loads under Minimum of a Priori Information: Statements, Classification and Interpretation,” Bulletin of Kiev National University, Mathematic, No. 2, 2004, Kiev, pp. 310-315.

[12] Yu. L. Menshikov, “Identification of Models of External Loads,” In: Book of Robotics, Automation and Control, Vienna, 2008.

[13] А. N. Tikhonov and V. Yu. Arsenin, “Methods of Incorrectly Problems Solution,” Science, Moscow, 1979.

[14] Yu. L. Menshikov, “Algorithms of Construction of Adequate Mathematical Description of Dynamic System,” Proceedings of MATHMOD 09 Vienna—Full Papers CD Volume, Vienna University of Technology, Vienna, February 2009, pp. 2482-2485.

[15] Yu. S. Osipov, A. V. Krajgimsky and V. I. Maksimov, “Methods of Dynamical Restoration of Inputs of Controlled Systems,” Ekaterinburg, 2011.

[16] Yu. L. Menshikov, “Inverse Problems in Non-Classical Statements,” International Journal of Pure and Applied Mathematics, Vol. 67, No. 1, 2011, pp. 79-96.

[17] Yu. L. Menshikov, “Uncontrollable Distortions of the Solutions Inverse Problems of Unbalance Identification,” Proceedings of ICSV12 XXII International Congress on Sound and Vibration, Lisbon, 11-14 July 2005, pp. 204-212.

[18] C. W. Groetsch, “Inverse Problems in the Mathematical Sciences,” Vieweg, 1993.

[19] A. V. Goncharskij, A. C. Leonov and A. G. Yagola, “About One Regularized Algorithm for Ill-Posed Problems with Approximate Given Operator,” Journal of Computational Mathematics and Mathematical Physics, Vol. 12, No. 6, 1972, pp. 1592-1594.

[20] Yu. L. Menshikov and N. V. Polyakov, “The Models of External Action for Mathematical Simulation,” Proceedings of 4th International Symposium on Systems Analysis and Simulation, Berlin, 1992, pp. 393-398.

[21] Yu. L. Menshikov and A. G. Nakonechnij, “Principle of Maximum Stability in Inverse Problems under Minimum a Priori Initial Information,” Proceedings of International Conference PDMU-2003, Kiev-Alushta, 8-12 September 2003, pp. 80-82.