Filiberto Fele

Filiberto Fele, Kostas Margellos

We consider a multi-agent noncooperative game with agents' objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We treat the Nash equilibrium computation problem within the realm of probably approximately correct (PAC) learning. Building upon recent developments in scenario-based optimization, we accompany the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected (in probabilistic terms) when a new uncertainty realization is encountered. For a wide class of games, we also show that the computation of the so called compression set - a key concept in scenario-based optimization - can be directly obtained as a byproduct of the proposed solution methodology. Finally, we illustrate how to overcome differentiability issues, arising due to the introduction of scenarios, and compute a Nash equilibrium solution in a decentralized manner. We demonstrate the efficacy of the proposed approach on an electric vehicle charging control problem.

Carlos Moreno-Blazquez, Filiberto Fele, Teodoro Alamo

The integration of renewable energy sources and distributed generation in the power system calls for fast and reliable predictions of grid dynamics to achieve efficient control and ensure stability. In this work, we present a novel nonparametric data-driven prediction algorithm based on kriging interpolation, which exploits the problem's numerical structure to achieve the required computational efficiency for fast real-time forecasting. Our results enable accurate frequency prediction directly from measurements, achieving sub-second computation times. We validate our findings on a simulated distribution grid case study.