Abstract
This paper solves a mean-field type hierarchical optimal control problem in electricity market. The authors consider n − 1 prosumers and one producer. The ith prosumer, for 1 < i < n, is a leader of the (i − 1)th prosumer and is a follower of the (i + 1)th prosumer. The first player (agent) is the follower at the bottom whereas the nth is the leader at the top. The problem is described by a linear jump-diffusion system of conditional mean-field type, where the conditioning is with respect to common noise, and a quadratic cost functional involving, the square of the conditional expectation of the controls of the agents. The authors provide a semi-explicit solution of the corresponding mean-field-type hierarchical control problem with common noise. Finally, the authors illustrate the obtained result via a numerical example with two different scenarios.
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Acknowledgements
We gratefully acknowledge support from Tamkeen under the NYU Abu Dhabi Research Institute grant CG002, and U.S. Air Force Office of Scientific Research under Grant No. FA9550-17-1-0259.
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This paper was recommended for publication by Editor GUO Jin.
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Frihi, Z.E.O., Choutri, S.E., Barreiro-Gomez, J. et al. Hierarchical Mean-Field Type Control of Price Dynamics for Electricity in Smart Grid. J Syst Sci Complex 35, 1–17 (2022). https://doi.org/10.1007/s11424-021-0176-3
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DOI: https://doi.org/10.1007/s11424-021-0176-3