Collective target tracking mean field control for electric space heaters

As part of a system wide optimization problem in smart grids it is required that the mean temperature of a massive number of space heating devices associated with energy storage follows a computed target temperature trajectory. The classical control approach is to compute the required signal centrally for each device and to send that signal. However, the corresponding computational and communication requirements can be forbidding. Instead, in this paper the presence of large numbers of heaters justifies the use of a decentralized mean field control based approach to the problem. A novel agent cost structure including an integral term is utilized for this purpose. The corresponding system of mean field equations is developed, a fixed point analysis is given, an e-Nash theorem is presented, and numerical simulation results are provided.