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Flow and storage volume regulation is essential for the adequate transport and management of energy resources in district heating systems. In this letter, we propose a novel and suitably tailored – decentralized – adaptive control scheme addressing this problem whilst offering closed-loop stability guarantees. We focus on a system configuration comprising multiple heat producers, consumers and storage tanks exchanging energy through a common distribution network, which are features of modern and prospective district heating installations. {\color{black}The proposed controller is based on passivity, backstepping and (indirect) adaptive control theory.

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