05. Antipina E.V., Mustafina S.A., Antipin A.F., Morozkin N.D. Algorithm for Solving the Problem of Optimal Control of a Chemical-Technological Process with Terminal Constraints

DOI: 10.15507/2658-4123.032.202203.410-422

Algorithm for Solving the Problem of Optimal Control of a Chemical-Technological Process with Terminal Constraints

Evgeniya V. Antipina
Junior Researcher of the Science and Innovation Department, Sterlitamak Branch of Bashkir State University (49 Prospekt Lenina, Sterlitamak 453103, Russian Federation), Cand.Sci. (Phys.-Math.), ORCID: https://orcid.org/0000-0002-8458-9638, Researcher ID: AAG-2956-2021, This email address is being protected from spambots. You need JavaScript enabled to view it.

Svetlana A. Mustafina
Vice-Rector for Science and Innovation, Head of the Chair of Mathematical Modeling, Bashkir State University (32 Zaki Validi St., Ufa 450076, Russian Federation), Dr.Sci. (Phys.- Math.), Professor, ORCID: https://orcid.org/0000-0002-6363-1665, Researcher ID: AAB-5713-2020, This email address is being protected from spambots. You need JavaScript enabled to view it.

Andrey F. Antipin
Associate Professor, Department of Applied Computer Science and Programming, Sterlitamak Branch of Bashkir State University (49 Prospekt Lenina, Sterlitamak 453103, Russian Federation), Cand.Sci. (Engr.), ORCID: https://orcid.org/0000-0002-9151-4167, This email address is being protected from spambots. You need JavaScript enabled to view it.

Nikolay D. Morozkin
President of Bashkir State University (32 Zaki Validi St., Ufa 450076, Russian Federation), Dr.Sci. (Phys.-Math.), Professor, This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract
Introduction. The problem of determining the optimal mode parameters during the mathematical modeling of chemical and technological processes is the most important. Numerical methods and algorithms for the solution provide the basis for developing software packages to calculate processes and their digital twins. The mathematical model of the chemical-technological process can be described by a system of differential equations, highlighting the phase variables that determine the state of the process, and the control parameters, which can be changed and thereby affect the course of the process. The aim of the work is to develop a numerical algorithm for solving the problem of optimal control of a chemical-technological process in the presence of terminal constraints and the constraints on the control parameter.
Materials and Methods. There was formulated the problem of optimal control in general terms. To solve it, the penalty method and method of artificial immune systems were applied. There was described a method for including constraints in the penalty function and for choosing a sequence of coefficients with which the penalty is taken. To overcome local extrema, a random choice of initial values of control parameters was used.
Results. The article presents a step-by-step numerical algorithm for solving the problem of optimal control of a chemical-technological process with terminal constraints. A computational experiment was carried out for a model example, as a result of which the structure of the optimal process control and the corresponding optimal trajectories of phase variables are determined. It is shown that the calculated solution of the optimal control problem consists with the solution obtained by the needle linearization method.
Discussion and Conclusion. The developed algorithm allows finding a numerical solution to the problem of optimal control of a chemical-technological process with terminal constraints. The solution does not depend on the choice of the initial approximation.

Keywords: optimal control problem, terminal constraints, penalty method, artificial immune systems, chemical-technological process

Funding: This study was performed within the state task from the Ministry of Science and Higher Education of the Russian Federation (scientific project code no. FZWU-2020-0027).

Conflict of interest: The authors declare no conflict of interest.

For citation: Antipina E.V., Mustafina S.A., Antipin A.F., Morozkin N.D. Algorithm for Solving the Problem of Optimal Control of a Chemical-Technological Process with Terminal Constraints. Engineering Technologies and Systems. 2022;32(3):410–422. doi: https:// doi.org/10.15507/2658-4123.032.202203.410-422

Contribution of the authors:
E. V. Antipina – setting the research goal, developing the algorithm, writing the text, drawing the conclusions.
S. A. Mustafina – scientific guidance, analyzing the research results, revising the text, correcting the conclusions.
A. F. Antipin – analyzing the literary data, developing the software, calculations.
N. D. Morozkin – correcting the literary analysis, revising the text, correcting the conclusions.

All authors have read and approved the final manuscript.

Submitted 06.06.2022; approved after reviewing 05.07.2022;
accepted for publication 20.07.2022

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