Differentiable Hybrid-Action Neural Feedback Control for District Heating Networks

Abstract

Many cyber-physical systems require control policies that combine continuous setpoints with discrete operational de- cisions, such as equipment switching, mode selection, or resource scheduling. Discrete actions are not differentiable, which ob- structs gradient-based policy training, while conventional mixed- integer formulations remain costly to solve online. This paper proposes a hybrid-action neural controller (HANC) in which a continuous branch, a categorical branch and a differentiable assembly layer jointly generate commands that satisfy complex actuator constraints by construction. Categorical decisions are handled using a straight-through Gumbel estimator, enabling the policy to be trained by backpropagation through time over full closed-loop rollouts. The proposed framework is deployed on a district heating network (DHN) featuring multiple heat generation units and stratified thermal energy storage. Its performance is evaluated on a simulation of a real DHN located at RSE SpA in Italy. The resulting policy jointly learns switching decisions and continu- ous operating setpoints. Under dynamic electricity pricing, the learned controller reduces operating cost by 30% compared to a rule-based industrial baseline. We also show that, compared with a deterministic straight-through relaxation, injecting noise during training achieves similar cost while reducing hard switching by an order of magnitude, and attribute this difference to the wider decision margins of the resulting policy.