Rose, MaximilianMaximilianRoseGernandt, HannesHannesGernandtFaulwasser, TimmTimmFaulwasserSchiffer, JohannesJohannesSchiffer2025-07-172025-07-172025IEEE Control Systems Letters 9: 1706-1711 (2025)https://hdl.handle.net/11420/56296District heating networks (DHNs) are crucial for decarbonizing the heating sector. Yet, their efficient and reliable operation requires the coordination of multiple heat producers and the consideration of future demands. Predictive and optimization-based control is commonly used to address this task, but existing results for DHNs do not account for time-varying problem aspects. Since the turnpike phenomenon can serve as a basis for model predictive control design and analysis, this paper examines its role in DHN optimization by analyzing the underlying optimal control problem with time-varying prices and demands. That is, we derive conditions for the existence of a unique time-varying singular arc, which constitutes the time varying turnpike, and we provide its closed-form expression. Additionally, we present converse turnpike results showing a exact time-varying case implies strict dissipativity of the optimal control problem. A numerical example illustrates our findings.en2475-1456202517061711Institute of Electrical and Electronics Engineers Inc.Energy systems | Optimal Control | Predictive control for linear systemsSocial Sciences::333: Economics of Land and Energy::333.7: Natural Resources, Energy and EnvironmentComputer Science, Information and General Works::005: Computer Programming, Programs, Data and SecurityJournal Article10.1109/LCSYS.2025.3582614Journal Article