Nadhir Ben Rached (University of Leeds) – Chance Constrained Stochastic Optimal Control with Applications

In this work, we seek an optimal short-term, continuous-time power procurement schedule to minimise operating expenditure and carbon footprint of cellular wireless networks equipped with energy storage capacity, and hybrid energy systems consisting of uncertain renewable energy sources. The network operator needs to ensure a certain QoS constraint with high probability. This probabilistic constraint prevents us from using dynamic programming to solve the continuous-time stochastic optimal control problem. We introduce a time-continuous Lagrangian relaxation approach tailored for real-time power procurement in cellular networks, overcoming tractability issues associated with probabilistic QoS constraints. The numerical solution procedure involves building an efficient upwind finite difference solver for the Hamilton--Jacobi--Bellman equation corresponding to the relaxed problem, and an effective stochastic sub-gradient method to efficiently navigate the stochastic problem structure. The proposed numerical approach is applied on a model cellular network base station based on the German power system and daily cellular traffic data. Our approach demonstrates computational efficiency, providing near-optimal solutions in practical timeframes.