A Scenario-Based Approach for Stochastic Economic Model Predictive Control with an Expected Shortfall Constraint

This paper presents a novel approach to stochastic economic model predictive control (SEMPC) that minimizes average economic cost while satisfying an empirical expected shortfall (EES) constraint to manage risk. A new scenario-based problem formulation ensuring controlled risk with high confidence while minimizing the average cost is introduced. The probabilistic guarantees is dependent on the number of support elements over the entire input domain, which is difficult to find for high-dimensional systems. A heuristic algorithm is proposed to find the number of support elements. Finally, an efficient method is presented to reduce the computational complexity of the SEMPC problem with an EES constraint. The approach is validated on a water distribution network, showing its effectiveness in balancing performance and risk.