On control reconstructions to management problems
Contributions to game theory and management, Tome 13 (2020), pp. 402-414.

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We present and discuss a new approach to solutions of control reconstruction problems in real time. The suggested solution based on necessary optimality conditions for auxiliary calculus of variation problems with concave-convex discrepancy functional.
Keywords: optimal control, nonlinear systems, control reconstruction, calculus of variation, concave-convex discrepancy.
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     author = {Nina N. Subbotina},
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Nina N. Subbotina. On control reconstructions to management problems. Contributions to game theory and management, Tome 13 (2020), pp. 402-414. http://geodesic.mathdoc.fr/item/CGTM_2020_13_a21/

[1] Bellman R., Dynamic Programming, Princeton University Press, Princeton, NJ, 1957 | MR | Zbl

[2] D'Autilia M. C., Sgura I., B. Bozzini, “Parameter identification in ODE models with oscillatory dynamics: a Fourier regularization approach”, Inverse Problems, 33:6 (2017), 124009 | DOI | MR | Zbl

[3] Krasovskii N. N., The Theory of Motion Control, Nauka, M., 1968 (in Russian) | MR

[4] Krasovskii N. N., A. I. Subbotin, Game-Theoretical Control Problems, Springer-Verlag, NY, 1988 | MR | Zbl

[5] Krupennikov E. A., “On Control Reconstruction Problems for Dynamic Systems Linear in Controls”, Frontiers of Dynamic Games. Game Theory and Management, eds. Petrosyan L. A., Mazalov V. V., N. A. Zenkevich, Birkhäuser, Boston, 2018, 89–120 | DOI | MR | Zbl

[6] Kryazhimskii A. V., Yu. S. Osipov, “Modelling of a control in a dynamic system”, Eng. Cybern., 21:2 (1984), 38–47 | MR

[7] Leitmann G., Optimization techniques: with applications to aerospace systems, 5, ed. Leitmann G., Academic Press, NY, 1962 | MR

[8] Letov A. M., Dynamics of Flight and Control, Nauka, M., 1969 (in Russian)

[9] Liu Y. C., Chen Y. W., Wang Y. T., Chang J. R., “A high-order Lie groups scheme for solving the recovery of external force in nonlinear system”, Inverse Problems in Science and Engineering, 26:12 (2018), 1749-1783 | DOI | MR | Zbl

[10] Michel A., “Deterministic and stochastic optimal control”, IEEE Trans. Automat. Contr., 22:6 (1977), 997–998 | DOI | MR

[11] Osipov Y. S., A. V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, Gordon and Breach, Amsterdam, 1995 | MR | Zbl

[12] Osipov Yu. S., Kryazhimskii A. V., V. I. Maksimov, “Some Algorithms for the Dynamic Reconstruction of Inputs”, Proc. Steklov Inst. Math., 275, Suppl. 1 (2011), 86–120 | DOI | MR

[13] Pontryagin L. S., Boltyansky V. G., Gamkrelidze R. V., E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Nauka, M., 1961 (in Russian) | MR

[14] Petrosjan L. A., N. A. Zenkevich, Game Theory, NY, 1996 | MR

[15] Sabatier P. C., “Past and future of inverse problems”, J. Math. Phys., 41 (2000), 4082 | DOI | MR | Zbl

[16] Subbotina N. N., “On solutions of navigation inverse problems in real time”, AIP Conference Proceedings, AIP Publishing, NY, 2019, 020019 | DOI

[17] Subbotina N. N., E. A. Krupennikov, “The method of characteristics in an identification problem”, Proc. Steklov Inst. Math., 299, Suppl. 1 (2017), 205–216 | DOI | MR

[18] Subbotina N. N., E. A. Krupennikov, “A Solution to Inverse Problems For Dynamic Control Systems”, AIP J. Proceed., 1997:1 (2018), 020006

[19] Subbotina N. N., T. B. Tokmantsev, “The Method of Characteristics in Inverse Problems of Dynamics”, Universal J. Contr. Autom., 1:3 (2013), 79–85

[20] Subbotina N. N., Tokmantsev T. B., E. A. Krupennikov,, “On the solution of inverse problems of dynamics of linearly controlled systems by the negative discrepancy method”, Proc. Steklov Inst. Math., 291 (2015), 253–262 | DOI | MR | Zbl

[21] Tikhonov A. N., “Solution of incorrectly formulated problems and the regularization method”, Sov. Math., Dok., 4 (1963), 1624–1627 | MR | Zbl