Solutions to the problem of mathematical and computer modeling of the air temperature control system in a residential building

This paper deals with the problem of mathematical modeling of the thermoregulation process in living space. On the basis of the second order continuous linear dynamic system model the standard controllable and standard observable models are constructed in order to determine the optimal model for solving the problem of thermoregulation by researching the properties of stability, complete controllability and complete observability of all three models. As a result, revealed that all models possess the properties of complete controllability and observability at any non–zero values of parameters. Consequently, all three models can be recommended for solving the problem of modeling the thermoregulation process. The optimal control problem was solved for one of models in order to minimize the energy consumption at a given time interval.