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We consider dynamical systems with a large number of agents that can store and trade a commodity such as electricity. We present a price-formation model consisting of constrained mean-field games where the price is a Lagrange multiplier for the supply vs. demand balance condition. We illustrate the model using real data of daily energy consumption in the UK. Then we present a Fourier approximation method for the solutions of first-order nonlocal mean-field games. We approximate the system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Time permitting, we discuss possible applications to price formation problems where prices depend on state and time.
Bio: Joao Saude received the B.Sc. in Aerospace engineering, the M.S. in Mathematics both from IST - University of Lisbon, Portugal, and the Ph.D. in Electrical and Computer Engineering from Carnegie Mellon University, U.S.A., in 2018, under the supervision of Prof. Soummya Kar (CMU) and co-advised by Diogo Gomes (KAUST, S.A.). After a period as a Research Scientist at J.P. Morgan A.I. research (NYC), he is now at Systems and Robotics Institute (ISR) in Lisbon. His research focuses on optimal control theory and mean-field games. His research interests include as well recommendation systems, computer vision, and explainability of graph neural networks.