Udc 17. 977+644. Bashkir State University, Republic of Bashkortostan

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UDC 517.977+644.4
Bashkir State University, Republic of Bashkortostan,
450075 Ufa, ul. Zaki Validi, 32 E-mail: [e-mail]
An algorithm for solving the optimal control problem with terminal constraints is developed. A statement
of the optimal control problem with terminal constraints and constraints on the control parameter is
given. A numerical algorithm for solving the formulated problem based on the penalty method and
genetic algorithms is described. A computational experiment was carried out for the reaction of obtaining
phthalic anhydride in order to achieve the maximum yield of the reaction product in the presence of
terminal restrictions. Optimal temperature conditions and optimal concentrations of reagents have been
obtained.
Keywords: optimal control problem, terminal constraints, method
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fines, genetic algorithms, phthalic anhydride production reaction.
AUTOMETRY. 2020. V. 56, No. 6
DOI: 10.15372/AUT20200615
c E. V. Antipina, S. I. Mustafina, A. F. Antipin, S. A. Mustafina
Introduction. Currently, among the problems of mathematical modeling of dynamic systems,
optimal control problems are of the greatest practical interest, in which restrictions can be imposed
not only on control parameters, but also on phase variables. If the constraints on the phase
variables are given at the final time of the system operation, then such a problem is a problem with
terminal constraints. These include problems of transferring a controlled system from the initial
point to the final one, boundary extremal problems, etc. In addition, problems with phase constraints
can be reduced to optimal control problems with terminal constraints by applying mathematical
reductions [1]. The presence of restrictions on phase variables complicates the solution of optimal
problems both in the theoretical study of the properties of optimal processes and in the
implementation of numerical solution algorithms. Therefore, the development of methods and
algorithms for solving this problem is an urgent problem and is of scientific and practical interest.
One of the approaches to solving this class of problems consists in obtaining exact necessary
optimality conditions and constructing computational procedures on their basis [2, 3]. However,
such computational procedures are rather laborious and difficult to apply [4]. Another approach
involves reducing a problem with constraints on phase variables to a problem without constraints
using the penalty method [5]. In this method, an auxiliary function is introduced into consideration
by adding a penalty for violating the constraints imposed on the phase variables to the control
quality criterion of the original problem. Then the problem of optimal control without restrictions
is solved, where the constructed auxiliary function acts as a control quality criterion.