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

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.