Optimization Methods and Control Theory

Research Article

DOI 10.25209/2079-3316-2024-15-4-43-54

A heuristic algorithm for one nonlinear optimal control problem

dedicated to our teacher, Professor V. I. Gurman on the 90th anniversary of his birth

Irina Viktorovna Rasina¹, Irina Sergeevna Guseva²

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

Abstract. The optimal control problem for one of the variants of a quasilinear system is considered. To solve it, the idea of Professor V. I. Gurman is used, who proposed to combine two variants of the expansion principle. One of them is the traditional Krotov approach, and the second is the penalty function method. The selected class of systems allows for an analytical study of the Krotov Lagrangian, which in turn leads to the formulation of the algorithm. The resulting algorithm is tested on two illustrative examples, for which minimizing sequences are constructed. The complexity of the calculations is comparable with methods based on the traditional expansion principle. The calculation results are illustrated by tables and graphs. (In Russian).

Keywords: sufficient Krotov optimality conditions, the expansion principle, quasi-linear systems

MSC-2020

49M25; 49K21, 49N99

For citation: Irina V. Rasina, Irina S. Guseva. A heuristic algorithm for one nonlinear optimal control problem. Program Systems: Theory and Applications, 2024, 15:4, pp. 43–54. (In Russ.). https://psta.psiras.ru/2024/4_43-54.

Full text of article (PDF): https://psta.psiras.ru/read/psta2024_4_43-54.pdf.

The article was submitted 11.09.2024; approved after reviewing 24.09.2024; accepted for publication 02.11.2024; published online 08.11.2024.