关于一类线性二次高斯量化均值场博弈

IF 4.8 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Rinel Foguen Tchuendom , Roland Malhamé , Peter E. Caines
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引用次数: 0

摘要

能源供应商面临着能源生产风险和大量同质客户,其能源价格的设计是总能源需求中与风险相关的量化值的时变函数,它通过总能源需求的均值进行一般化定价。在无限人口极限中,我们用一类线性二次高斯量化均值场博弈来模拟定价问题。对于这些量化均值场博弈,我们证明了揭示价格轨迹的均衡的存在性和唯一性,以及将量化均值场博弈的反馈控制函数应用于大型但有限博弈时的近似纳什特性,并提供了纳什偏差趋近于零的速率与人口数量和数量级的函数关系。最后,在家庭加热器和使用太阳能发电的能源提供商的等效热参数模型中说明了这一类量化均值场博弈的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On a class of linear quadratic Gaussian quantilized mean field games

An energy provider faced with energy generation risks and a large homogeneous pool of customers designs its energy price as a time-varying function of a risk-related quantile of the total energy demand, which generalizes pricing through the mean of the total energy demand. In the infinite population limit, we model the pricing problem with a class of linear quadratic Gaussian quantilized mean field games. For these quantilized mean field games, we show existence and uniqueness of an equilibrium which reveals the price trajectory, as well as an approximate Nash property when the quantilized mean field game’s feedback control functions are applied to the large but finite game and the rate of convergence of the Nash deviation to zero as a function of the population size and the quantile is provided. Finally, the use of this class of quantilized mean field games is illustrated in the context of equivalent thermal parameter models for households heater and an energy provider using solar generation.

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来源期刊
Automatica
Automatica 工程技术-工程:电子与电气
CiteScore
10.70
自引率
7.80%
发文量
617
审稿时长
5 months
期刊介绍: Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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