## SYNTHESIS OF ZONAL CONTROL OF LUMPED SOURCES FOR THE HEAT CONDUCTION PROCESS

Volume 3 (2), December 2020, Pages 207-222

Samir Z. Guliyev

High Performance Computing Research Advance Center, Department of General and Applied Mathematics, Azerbaijan State Oil and Industry University, Baku, Azerbaijan; Institute of Control Systems of Azerbaijan National Academy of Sciences, Baku, Azerbaijan, This email address is being protected from spambots. You need JavaScript enabled to view it.

# Abstract

The paper studies the problem of synthesis of control of lumped sources for an object with distributed parameters based on discrete observation of the phase state at specific object points. We propose an approach in which the whole phase space at the observed points is preliminarily divided in some way into given subsets (zones). The synthesized controls are selected from the class of piecewise-constant functions, and their current values are determined by a subset of the phase space containing the population of current states of the object at the observed points, at which controls take constant values. Such synthesized controls are called zonal. We give a numerical technique for obtaining optimal values of zonal controls using efficient first-order optimization methods. To this purpose, we derive formulas for the gradient of the objective function in the space of zonal controls.

Keywords:

Synthesis of Control, Zonal Control, Feedback, Distributed System, Heat Equation, the Gradient of Functional.

DOI: https://doi.org/10.32010/26166127.2020.3.2.207.222

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