A class of collective target tracking problems in energy systems: Cooperative versus non-cooperative mean field control solutions

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 follow a precomputed target temperature trajectory. The classical control approach is to evaluate the required signal centrally for each device and to send that signal. However, the corresponding computational and communication requirements can be forbidding. In previous work [1] an integral error based decentralized mean field control approach was followed, the corresponding system of mean field equations was developed, and an ∈-Nash theorem was presented. In this work a cooperative mean field formulation [2] is utilized whereby the resulting set of strategies asymptotically achieves the social optimum as N → ∞. The corresponding system of mean field equations is developed, an ∈-Nash theorem is presented, and numerical simulations are provided for comparing results based on the two approaches.