###### Search for the optimal control of the petrochemical processes with terminal constraints based on the differential evolution method

UDC: 519.6:004.4

DOI: 10.33285/2782-604X-2023-2(595)-31-36

Authors:

ANTIPINA EVGENIA V.^{1},

MUSTAFINA SVETLANA A.^{1},

ANTIPIN ANDREY F.^{1}
^{1} Ufa University of Science and Technology, Ufa, Russia

Keywords: optimal control, penalty method, differential evolution, terminal constraints, petrochemical process, maximum principle, optimal trajectory

Annotation:

The article is devoted to the development of a method for solving the problem of optimal control over a petrochemical process with terminal constraints. The optimal control problem with terminal constraints and constraints on the control parameter is formulated in general terms. A method for solving the set problem based on the penalty method and the differential evolution method is presented. The penalty method reduces a problem with terminal constraints to an optimal control problem that does not contain constraints imposed on phase variables. To solve the new problem, the application of the differential evolution method is proposed. A computational experiment was carried out as a model example, as a result of which the vector of the optimal process control and the corresponding vectors of phase variables were calculated. The numerical solution of the optimal control problem with terminal constraints is compared with the solution obtained using the Pontryagin maximum principle. It is shown that the solution calculated by the evolutionary method agrees satisfactorily with the analytical solution.

Bibliography:

1. Stepashina E.V., Mustafina S.A. Chislennyy algoritm utochneniya mekhanizma khimicheskoy reaktsii DRGEP-metodom // Zhurn. Srednevolzhskogo mat. o-va. – 2011. – T. 13, № 3. – S. 118–121.

2. Dikusar V.V., Milyutin A.A. Kachestvennye i chislennye metody v printsipe maksimuma / otv. red. M.A. Krasnosel'skiy. – M.: Nauka, 1989. – 144 s.

3. Gornov A.Yu. Algoritmy resheniya zadach optimal'nogo upravleniya s terminal'nymi ogranicheniyami // Vychislitel'nye tekhnologii. – 2008. – T. 13, № 4. – S. 44–50.

4. Karpenko A.P. Evolyutsionnye operatory populyatsionnykh algoritmov global'noy optimizatsii // Matematika i mat. modelirovanie. – 2018. – № 1. – S. 59–89. – DOI: 10.24108/mathm.0118.0000103

5. Self-adaptive differential evolution algorithm with improved mutation strategy / Shihao Wang, Yuzhen Li, Hongyu Yang, Hong Liu // Soft Computing. – 2018. – Vol. 22, Issue 10. – P. 3433–3447. – DOI: 10.1007/s00500-017-2588-5

6. Mohamed A.W., Mohamed A.K. Adaptive guided differential evolution algorithm with novel mutation for numerical optimization // Int. J. of Machine Learning and Cybernetics. – 2019. – Vol. 10, Issue 2. – P. 253–277. – DOI: 10.1007/s13042-017-0711-7

7. Panteleev A.V., Letova T.A. Metody optimizatsii v primerakh i zadachakh: ucheb. posobie. – M.: Vysshaya shk., 2005. – 544 s.

8. Chislennyy algoritm resheniya zadachi optimal'nogo upravleniya s terminal'nymi ogranicheniyami dlya dinamicheskikh sistem / E.V. Antipina, S.I. Mustafina, A.F. Antipin, S.A. Mustafina // Avtometriya. – 2020. – T. 56, № 6. – S. 132–140. – DOI: 10.15372/AUT20200615

9. Antipina E.V., Mustafina S.A., Antipin A.F. Chislennyy algoritm identifikatsii kineticheskoy modeli khimicheskoy reaktsii // Vestn. Tekhnolog. un-ta. – 2019. – T. 22, № 9. – S. 13–17.

10. Panteleev A.V., Bortakovskiy A.S. Teoriya upravleniya v primerakh i zadachakh. – M.: Vysshaya shk., 2003. – 583 s.