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Title: On Reverse Stackelberg Game and Optimal Mean Field Control for a Large Population of Thermostatically Controlled Loads

Abstract

This paper studies a multi-stage pricing problem for a large population of thermostatically controlled loads. The problem is formulated as a reverse Stackelberg game that involves a mean field game in the hierarchy of decision making. In particular, in the higher level, a coordinator needs to design a pricing function to motivate individual agents to maximize the social welfare. In the lower level, the individual utility maximization problem of each agent forms a mean field game coupled through the pricing function that depends on the average of the population control/state. We derive the solution to the reverse Stackelberg game by connecting it to a team problem and the competitive equilibrium, and we show that this solution corresponds to the optimal mean field control that maximizes the social welfare. Realistic simulations are presented to validate the proposed methods.

Authors:
; ; ;
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1339897
Report Number(s):
PNNL-SA-109052
DOE Contract Number:
AC05-76RL01830
Resource Type:
Conference
Resource Relation:
Conference: 2016 American Control Conference, July 6-8, 2016, Boston, MA
Country of Publication:
United States
Language:
English

Citation Formats

Li, Sen, Zhang, Wei, Lian, Jianming, and Kalsi, Karanjit. On Reverse Stackelberg Game and Optimal Mean Field Control for a Large Population of Thermostatically Controlled Loads. United States: N. p., 2016. Web. doi:10.1109/ACC.2016.7525463.
Li, Sen, Zhang, Wei, Lian, Jianming, & Kalsi, Karanjit. On Reverse Stackelberg Game and Optimal Mean Field Control for a Large Population of Thermostatically Controlled Loads. United States. doi:10.1109/ACC.2016.7525463.
Li, Sen, Zhang, Wei, Lian, Jianming, and Kalsi, Karanjit. 2016. "On Reverse Stackelberg Game and Optimal Mean Field Control for a Large Population of Thermostatically Controlled Loads". United States. doi:10.1109/ACC.2016.7525463.
@article{osti_1339897,
title = {On Reverse Stackelberg Game and Optimal Mean Field Control for a Large Population of Thermostatically Controlled Loads},
author = {Li, Sen and Zhang, Wei and Lian, Jianming and Kalsi, Karanjit},
abstractNote = {This paper studies a multi-stage pricing problem for a large population of thermostatically controlled loads. The problem is formulated as a reverse Stackelberg game that involves a mean field game in the hierarchy of decision making. In particular, in the higher level, a coordinator needs to design a pricing function to motivate individual agents to maximize the social welfare. In the lower level, the individual utility maximization problem of each agent forms a mean field game coupled through the pricing function that depends on the average of the population control/state. We derive the solution to the reverse Stackelberg game by connecting it to a team problem and the competitive equilibrium, and we show that this solution corresponds to the optimal mean field control that maximizes the social welfare. Realistic simulations are presented to validate the proposed methods.},
doi = {10.1109/ACC.2016.7525463},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 7
}

Conference:
Other availability
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