A level-set approach for control problems arising in energy production and distribution
The consumption of energy amongst a population often exhibits heterogeneous features, including but not limited to geographical, demographic and seasonality factors. Matching supply and demand is imperative for stable and reliable transmission of electricity to customers. We model such a problem in terms of a state-constrained extended mean-field control problem. Given a target set of consumption profiles, the backwards reachable set can be characterised by the zero-level set of a solution of a Master Bellman equation. The backwards reachable set may be approximated by considering a suitable discretisation of the value function that corresponds to an approximating finite player game. The resulting finite-dimensional HJB equation can be computed with deep learning-based numerical methods.
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Keywords: Master Bellman equation, HJB equation, deep learning-based numerical methods.
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