(КПІ ім. Ігоря Сікорського, 2024) Stenin, A.; Pasko, V.; Soldatova, M.; Drozdovich, I.
Currently, there is a large number of objects related to recirculation of material flows, mixing of reagents of liquid and gaseous media, etc. Among them are heat supply systems of residential buildings. Their dynamics are described by differential equations with a deviating argument. Optimizing the operation of such objects using known methods is quite difficult. This paper proposes a dummy variable method for reducing the original system of differential equations with a deviating argument to a system of ordinary differential equations and transfer equations for which known optimization methods can be applied. The method is generalized to systems with a non-stationary deviating argument and to systems with several processes having an aftereffect. The practical use of the dummy variable method is shown on the example of solving the problem of optimal control of the heat exchange process in a private residential building.