Abstract
In the present paper an optimal control problem for a concrete system of differential-algebraic equations (DAEs) is considered. This problem arises in the dynamic optimization of unsteady district heating networks. Based on the Carathéodory theory existence of a unique solution to the specific DAE system is proved using specific properties of the considered district heating network model. Moreover, it is shown that the optimal control problem possesses optimal solutions. For the numerical experiments different networks are considered including also data from a real district heating network.
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