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ISSN 2079-3316 Bilingual online scientific Online scientific journal of the Ailamazyan Program System Institute of the Ailamazyan PSI of PSI of Russian Academy of Science of RAS 12+ 
Volume 16 (2025) . Issue 3 (66) . Paper No. 2 (449)

Optimization Methods and Control Theory

Research Article
DOIDigital Object Identifier 10.25209/2079-3316-2025-16-3-23-40

Strong control improvement method for non-homogeneous discrete systems

Irina Viktorovna Rasina1Correspondent author, Irina Sergeevna Guseva2

1Ailamazyan Program Systems Institute of RAS, Ves'kovo, Russia
2Buryat State University, Ulan-Ude, Russia
1 Irina Viktorovna Rasina — Correspondent author irinarasina@gmail.com

Abstract. The class of non-homogeneous discrete systems (NDS) with intermediate criterions is considered. These systems are two-level and are prevalent in practice. They can be also obtained via discretization of continuous systems in the process of solving optimization problems using iterative methods. For this class of systems a strong improvement method of the second order is constructed based on the analogue of Krotov type sufficient optimality conditions.

The authors of the article question the assertion that for classical discrete control systems, as well as for heterogeneous ones, there is no sense in introducing the concept of a strong relative minimum. Therefore, when constructing an improvement method, we put forward the requirement of proximity of neighboring approximations from the class of admissible only by the process states at both levels. The resulting method contains a vector-matrix two-level system for conjugate variables. The increment of controls at each level linearly depends on the corresponding states, which allows finding a solution in the form of approximate linear synthesis of optimal control.

The method was tested on two illustrative examples, which showed its efficiency. The application of the developed method to a more complex example allowed us to obtain a smaller value of the functional than that found earlier by a similar in structure minimax improvement method. (In Russian).

Keywords: non-homogeneous discrete systems, intermediate criterions, optimal control

MSC-20202020 Mathematics Subject Classification 49M99; 49K99MSC-2020 49-XX: Calculus of variations and optimal control; optimization MSC-2020 49Mxx: Numerical methods in optimal control MSC-2020 49M99: None of the above, but in this section MSC-2020 49Kxx: Optimality conditions

For citation: Irina V. Rasina, Irina S. Guseva. Strong control improvement method for non-homogeneous discrete systems. Program Systems: Theory and Applications, 2025, 16:3, pp. 23–40. (In Russ.). https://psta.psiras.ru/2025/3_23-40.

Full text of article (PDF): https://psta.psiras.ru/read/psta2025_3_23-40.pdf.

The article was submitted 04.04.2025; approved after reviewing 27.05.2025; accepted for publication 09.07.2025; published online 19.07.2025.

© Rasina I. V., Guseva I. S.
2025
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