Open AccessSYNTHESIS OF ZONAL CONTROL OF LUMPED SOURCES FOR THE HEAT CONDUCTION PROCESS
Author(s) -
S. Z. Kuliev,
Azerbaijan State Oil
Publication year - 2020
Publication title -
azerbaijan journal of high performance computing
Language(s) - English
Resource type - Journals
eISSN - 2617-4383
pISSN - 2616-6127
DOI - 10.32010/26166127.2020.3.2.207.222
Subject(s) - piecewise , constant (computer programming) , object (grammar) , thermal conduction , class (philosophy) , function (biology) , space (punctuation) , phase space , population , mathematics , phase (matter) , constant function , current (fluid) , process (computing) , control theory (sociology) , mathematical optimization , control (management) , mathematical analysis , computer science , physics , thermodynamics , demography , quantum mechanics , artificial intelligence , evolutionary biology , sociology , biology , programming language , operating system
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.