Mean field game methodologies appeared about a decade ago as the result of independent research efforts in Applied Mathematics (Finance, Lions‐Lasry France), and Control Engineering ( Power control of cellular telephones, Huang‐Caines‐ Malhamé). A closely related concept, oblivious equilibrium, was also proposed in the context of Management Science (Weintraub, Benkard, Van Roy). Mean Field Games are essentially dynamic games involving a very large number of players, interacting anonymously, with the influence of each vanishing as their total number grows without bound. It is the major simplifications associated with the infinite population situation, used as a proxy to the large but finite population situation, which make this methodology so promising as far as applications are concerned. The potential applications range from reproducing with simple decentralized control laws herd and swarms dynamics, understanding opinions propagation, developing decentralized collective decision making mechanisms, understanding price fluctuations in an economy, etc.
In this talk, after a brief exposition of the main ideas behind Mean Field Game theory, we consider applications to a novel set of problems arising in energy systems. Due to increasing rates of penetration of intermittent renewable energy sources such as solar and wind energy in power systems, the fluctuations of instantaneous mismatches between generation and electricity demand have drastically augmented. Besides the attending network stability problems, this has deferred an increasing compensatory role to the so‐called spinning reserves in power systems; the latter typically rely on environmentally damaging fossil fuels. As an alternative, we aim at creating a control architecture that would allow the harnessing of the energy storage capability associated with millions of electrical devices such as electric water heaters, air conditioners, electric space heaters in dwellings and commercial buildings into a gigantic but distributed battery to smooth the generation‐load mismatch fluctuations, while maintaining local customer comfort and safety constraints. We develop novel formulations of the current mean field game theory that could help in achieving that goal. Numerical results are reported.
This is joint work with Arman Kizilkale.
Biography of Roland Malhamé
Roland Malhamé received the Bachelor’s, Master’s and Ph.D. degrees in Electrical Engineering from the American University of Beirut, the University of Houston, and the Georgia Institute of Technology in 1976, 1978 and 1983 respectively.
After single year stays at University of Quebec , and CAE Electronics Ltd (Montreal), he joined in 1985 École Polytechnique de Montréal, where he is Professor of Electrical Engineering. In 1994, 2004, and 2012 he was on sabbatical leave respectively with LSS CNRS (France), École Centrale de Paris, , and University of Rome Tor Vergata.
His interest in statistical mechanics inspired approaches to the analysis and control of large scale systems has led
him to contributions in the area of aggregate electric load modeling, and to the early developments of the theory of mean field games.
His current research interests are in stochastic control, and the analysis and optimization of complex networks, in particular manufacturing, communication and power system networks. From june 2005 to june 2011, he was director of Groupe d’Études et de Recherche en Analyse des Décisions. He is an Associate Editor of International Transactions on Operations Research.