| Rashad Mamedov, Sardar Gasimov Synthesis of Optimal Control for the Heat Propagation Process in Rarefied Media with Conductive Viscosity |
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| Abstract. The problem of building an optimal regulator in the process of heat exchange in viscous heat-conducting gaseous medium is considered. In this case, not only the heat transfer density, but also the velocity of heat transfer changes depends on temperature gradient. Moreover, as we consider a medium with temperature viscosity, we have to take into account the velocity of changes in temperature gradient. Therefore, the mathematical model of the considered process is a third order partial differential equation. The minimized functional is quadratic. The solution of the corresponding boundary value problem is sought in the form of Fourier series, therefore we restate our problem in infinite-dimensional phase space. To solve the newly obtained problem, we use the dynamic programming method, and we derive the optimal control in the form of synthesis. |
| Keywords: optimal regulator, gaseous medium, dynamic programming method |
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