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<p>We consider an approximation of an optimal control problem in the class of piecewise constant controls in the form of a finite-dimensional optimization problem. In the finite-dimensional problem obtained, an optimality condition is constructed as a fixed-point problem for a special control operator. To solve the fixed-point problem numerically, we construct an iterative method whose complexity at each iteration is estimated by solving two Cauchy problems. The effectiveness of the approach proposed for the approximate solution of the optimization problem for a multistage process is illustrated by an example.</p>

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THE METHOD OF PIECEWISE CONSTANT APPROXIMATION OF CONTROL IN PROBLEMS OF OPTIMIZATION OF MULTISTAGE PROCESSES

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • A. S. Buldaev,
  • V. Yu. Kurokhtin

摘要

We consider an approximation of an optimal control problem in the class of piecewise constant controls in the form of a finite-dimensional optimization problem. In the finite-dimensional problem obtained, an optimality condition is constructed as a fixed-point problem for a special control operator. To solve the fixed-point problem numerically, we construct an iterative method whose complexity at each iteration is estimated by solving two Cauchy problems. The effectiveness of the approach proposed for the approximate solution of the optimization problem for a multistage process is illustrated by an example.