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The paper studies the problem of feedback control of the power of point sources for rod heating and of moving sensors that measure the state of the rod. The locations of the sources are optimized, and the values of their power at each instant of time are determined with respect to the measured values of the rod temperature. The velocities of the sensors are also determined based on the results of current measurements. The types of functional dependencies of controlled actions on measured state values, including unknown (optimized) feedback parameters, are proposed and investigated. The differentiability of the objective functional is proven and constructive formulas are obtained for the components of the gradient of the objective functional with respect to the optimized feedback parameters and the locations of the sources on the rod are obtained. Numerical results of the solution of the test problem was presented.

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Synthesis of Control of Sensors’ Motion and Rod Heating Sources’ Power with Optimization of Their Placement

  • 会议论文

  • 发表日期：

    2025年

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  • Kamil R. Aida-zade,
  • Vugar A. Hashimov

摘要

The paper studies the problem of feedback control of the power of point sources for rod heating and of moving sensors that measure the state of the rod. The locations of the sources are optimized, and the values of their power at each instant of time are determined with respect to the measured values of the rod temperature. The velocities of the sensors are also determined based on the results of current measurements. The types of functional dependencies of controlled actions on measured state values, including unknown (optimized) feedback parameters, are proposed and investigated. The differentiability of the objective functional is proven and constructive formulas are obtained for the components of the gradient of the objective functional with respect to the optimized feedback parameters and the locations of the sources on the rod are obtained. Numerical results of the solution of the test problem was presented.