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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 53

Development of Methods for Solving Linear-Quadratic Optimal Control Problems in the Scholarly Works of Professor V. A. Srochko (to the 80th Anniversary of His Birth)

Author(s)

Vladimir G. Antonik1, Alexander V. Arguchintsev1

1 Irkutsk State University, Irkutsk, Russian Federation

Abstract
The paper provides a brief review of some results obtained in the study of linear-quadratic optimal control problems by one of the founders of the Irkutsk school of optimal control Professor V. A. Srochko.
About the Authors

Vladimir G. Antonik, Cand. Sci. (Phys.Math.), Assoc. Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, vga@math.isu.ru 

Alexander V. Arguchintsev, Dr. Sci. (Phys.Math.), Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, arguch@math.isu.ru

For citation
Antonik V. G., Arguchintsev A. V. Development of Methods for Solving Linear-Quadratic Optimal Control Problems in the Scholarly Works of Professor V. A. Srochko (to the 80th Anniversary of His Birth). The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 53, pp. 165–172. (in Russian) https://doi.org/10.26516/1997-7670.2025.53.165
Keywords
optimal control, linear-quadratic problems, parameterization, computational methods
UDC
012
MSC
01А70
DOI
https://doi.org/10.26516/1997-7670.2025.53.165
References
  1. Antonik V.G., Arguchintsev A.V. To the 75th anniversary of the birth of professor V. A. Srochko. The Bulletin of Irkutsk State University. Series Mathematics, 2020, vol. 34, pp. 126-134. https://doi.org/10.26516/1997-7670.2020.34.126 (in Russian)
  2. Antonik V.G., Srochko V.A. The solution of optimal control problems using linearization methods. Comput. Math. Math. Phys., 1992, vol. 32, no. 7, pp. 859–871. (in Russian) 
  3. Antonik V.G., Srochko V.A. The projection method in linear-quadratic problems of optimal control. Comput. Math. Math. Phys., 1998, vol. 38, no. 4, pp. 543–551. (in Russian) 
  4. Arguchintsev A.V., Dykhta V.A., Srochko V.A. Optimal control: nonlocal conditions, computational methods, and the variational principle of maximum. Russian Math., 2009, vol. 53, no. 1, pp. 1–35. https://doi.org/10.3103/S1066369X09010010 (in Russian)
  5. Arguchintsev A.V., Srochko V.A. Procedure for regularization of bilinear optimalcontrol problems based on a finite-dimensional model. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2022, vol. 18, iss. 1, pp. 179–187. https://doi.org/10.21638/11701/spbu10.2022.115 (in Russian) 
  6. Srochko V.A. The phase linearization method in optimal control problems with a free right end. Russian Math., 1992, vol. 36, no. 7, pp. 68–75. (in Russian) 
  7. Srochko V.A. The quadratic phase approximation method for solving optimal control problems. Russian Math., 1993, vol. 37, no. 12, pp. 81–88. (in Russian) 
  8. Srochko V.A. Iteratsionnye metody resheniya zadach optimal’nogo upravleniya [Iterative Solution of Optimal Control Problems]. Moscow, FIZMATLIT Publ., 2000, 160 p. (in Russian) 
  9. Srochko V.A., Aksenyushkina E.V. Parametric transformation of nonconvex optimal control problems Itogi Nauki i Tekhniki. Sovremennaya Matematika i Priljzheniya. Tematicheskie Obzory VINITU, 2025, vol.241, pp. 64–70. https://doi.org/10.36535/2782-4438-2025-241-64-70 (in Russian) 
  10. Srochko V.A., Arguchintsev A.V. Parametric regularization of the functional in a linear-quadratic optimal control problem. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 49, pp. 32–44. https://doi.org/10.26516/1997- 7670.2024.49.32 (in Russian) 
  11. Srochko V.A., Dushutina S.N., Pudalova E.I. Regularization of the maximum principle and of improvement methods in quadratic optimal control problems. Russian Math., 1998, vol. 42, no. 12, pp. 77–87. (in Russian) 
  12. Srochko V.A., Mamonova N.V. Iterative procedures for solving optimal control problems based on quasigradient approximations. Russian Math., 2001, vol. 45, no. 12, pp. 52–64. (in Russian) 
  13. Srochko V.A., Pudalova E.I. Methods for the nonlocal improvement of admissible controls in linear problems with delay. Russian Math., 2000, vol. 44, no. 12, pp. 76–86. (in Russian) 
  14. Srochko V.A., Ushakova S.N. The method of complete quadratic approximation in optimal control problems. Russian Math., 2004, vol. 48, no. 1, pp. 85–90. (in Russian)

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