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

xi,
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äîëÿ
xi,
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äîëÿ
0,6
0,4
0
0,8
0,2
0,1
0
1,0
0,2
0,8 t, ÷
0,2
0,6
0,8 t, ÷
0,4
0,4
0,6
0,2
X1
X3
X4
X5
x2
Rice. Fig. 1. Dynamics of optimal concentrations of substances in the reaction of obtaining
phthalic anhydride (X1 is naphthalene, X2 is naphthoquinone, X3 is phthalic anhydride)
Rice. Fig. 2. Dynamics of optimal substances for the reaction of obtaining phthalic
anhydride (X4 is carbon dioxide, X5 is maleic anhydride)
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E. V. Antipina, S. I. Mustafina, A. F. Antipin, S. A. Mustafina
139
Conclusion. The developed algorithm for solving the optimal control problem with terminal
constraints makes it possible to find a numerical solution in an acceptable time, regardless of the
choice of the initial approximation. Since stepwise actions are based on the principle of operation
of a genetic algorithm, such an algorithm makes it possible to overcome a number of difficulties
that arise in solving optimization problems, such as the nonlinearity of the mathematical
description of processes, the large dimension of the problem, and the requirements for the
continuity of the objective function and its derivatives.
the algorithm can be applied to problems of finding optimal control with terminal
constraints and for other processes that are described by nonlinear systems of differential equations.
Using the program that implements the algorithm presented in this work, a computational
experiment was carried out for the reaction of obtaining phthalic anhydride. The optimal temperature
regime was determined, which provides the maximum value of the reaction product (phthalic
anhydride) at the final time point under the given restrictions. The optimal concentrations of the
reagents were calculated. It is shown that the concentration of phthalic anhydride calculated under
the optimal temperature regime exceeds the values of the concentrations calculated at other
temperatures, and the limitations of the phase variables at the final moment of time are satisfied.
Designed