A level-set approach for control problems arising in energy production and distribution

Abstract

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 viscosity 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.

Our Speaker

Athena Picarelli is a Full Professor at the Department of Economics at the University of Verona. She earned her PhD in Applied Mathematics from ENSTA ParisTech (École Nationale Supérieure de Techniques Avancées) in Paris. She then completed a two-year postdoctoral fellowship at the University of Oxford (Nomura Fellowship) and a one-year postdoctoral position at Imperial College London (CFM Fellowship). She joined the University of Verona in 2018. Her research interests include stochastic optimal control, Hamilton-Jacobi-Bellman equations, numerical methods for partial differential equations, and computational finance.