Abstract
For optimal control problems, a new approach based on the search for an extremum of a special functional is proposed. The differential problem is reformulated as an ill-posed variational inverse problem. Taking into account ill-posedness leads to a stable numerical minimization procedure. The method developed has a high degree of generality, since it allows one to find special controls. Several examples of interest concerning the solution of classical optimal control problems are considered.
Similar content being viewed by others
References
Yu. S. Osipov and A. V. Kryazhimskii, Inverse Problems for Ordinary Differential Equations: Dynamical Solutions (Gordon and Breach, London, 1995).
A. B. Kurzhanski, Control and Observation under Uncertainty (Nauka, Moscow, 1977) [in Russian].
M. M. Khapaev and T. M. Khapaeva, Math. Notes 97 (4), 616–620 (2015).
T. M. Khapaeva, Appl. Comput. Math. 3 (4), 117–120 (2014).
C. Marchal, J. Optim. Theory Appl. 11 (5), 441–468 (1973).
G. Borg, Acta Math. 78 (1), 1–96 (1946).
D. E. Okhotsimskii, Prikl. Mat. Mekh. 10 (2), 251–272 (1946).
R. H. Goddard, A Method of Reaching Extreme Altitudes, Smithsonian Miscellaneous Collections (Smithsonian Institution, 1919), Vol. 71, no.2.
A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Halsted, New York, 1977; Nauka, Moscow, 1979).
M. I. Zelikin and L. A. Manita, J. Math. Sci. 151 (6), 3506–3542 (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Ternovskii, M.M. Khapaev, T.M. Khapaeva, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 4.
Rights and permissions
About this article
Cite this article
Ternovskii, V.V., Khapaev, M.M. & Khapaeva, T.M. Application of the Variational Method for Solving Inverse Problems of Optimal Control. Dokl. Math. 98, 603–606 (2018). https://doi.org/10.1134/S1064562418070219
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562418070219