[论文解读] Nash equilibria in electric vehicle charging control games: Decentralized computation and connection with social optima

Luca Deori, Kostas Margellos+1 more|arXiv (Cornell University)|Dec 5, 2016

Electric Vehicles and Infrastructure被引用 3

一句话总结

本文将电动汽车（EV）充电建模为具有异质约束的多智能体博弈，证明了唯一纳什均衡的存在性，并表明该均衡对应于一个辅助优化问题的解。当电动汽车数量趋于无穷大时，纳什均衡收敛至社会最优解，且通过正则化雅可比算法可实现均衡的精确分布式计算。

ABSTRACT

We consider the problem of optimal charging of plug-in electric vehicles (PEVs). We treat this problem as a multi-agent game, where each vehicle/agent is subject to possibly different constraints. Under this set-up, we show that, for any finite number of possibly heterogeneous agents, the PEV charging control game admits a unique Nash equilibrium, which is the optimizer of an auxiliary minimization program. To characterize the population of heterogeneous PEVs as its size grows to infinity, we assume that the parameters defining the constraints of each vehicle are drawn randomly from a given distribution. We are then able to show that, as the number of agents tends to infinity, the value of the game and the social optimum of the cooperative counterpart of the problem under study coincide for almost any choice of the random heterogeneity parameters. Moreover, in the case of a discrete probability distribution, we provide a systematic way to abstract agents in homogeneous groups and show that the effect of heterogeneity averages out as their number tends to infinity. We also show that, for any finite number of agents, the desired Nash equilibrium can be computed exactly by means of a regularized Jacobi algorithm, and support our theoretical results via a detailed simulation study.

研究动机与目标

• 将插电式电动汽车（PEV）充电控制建模为具有异质约束的多智能体博弈。
• 建立PEV充电控制博弈中纳什均衡的存在性与唯一性。
• 分析当智能体数量趋于无穷大时，该博弈的渐近行为。
• 为有限规模群体开发一种计算纳什均衡的分布式算法。
• 证明在大规模异质智能体群体下，纳什均衡收敛至社会最优解。

提出的方法

• 将PEV充电控制问题建模为具有个体约束的异质智能体之间的非合作博弈。
• 证明纳什均衡是辅助凸最小化问题的唯一解。
• 假设智能体参数是从给定概率分布中独立同分布抽取的，以建模大规模异质性。
• 利用大数定律与遍历性论证，证明随着智能体数量增加，博弈值收敛至社会最优解。
• 引入正则化雅可比算法，以确保在有限群体中实现纳什均衡的收敛计算。
• 当分布为离散时，将异质智能体抽象为同质群体，从而实现可扩展计算。

实验结果

研究问题

• RQ1 在具有异质约束的多智能体PEV充电博弈中，是否存在唯一的纳什均衡？
• RQ2 当PEV数量趋于无穷大时，纳什均衡的值如何变化？
• RQ3 在大规模异质PEV群体的极限下，纳什均衡在多大程度上收敛至社会最优解？
• RQ4 对于有限数量的智能体，能否以分布式方式计算纳什均衡？
• RQ5 智能体异质性如何影响整体系统结果？是否可将其抽象为同质群体？

主要发现

• 对于任意有限数量的异质PEV，均存在唯一纳什均衡，且该均衡对应于一个辅助凸最小化问题的解。
• 当智能体数量趋于无穷大时，纳什均衡的值几乎必然收敛至社会最优解，无论随机异质性参数的具体实现如何。
• 当智能体参数分布为离散时，可将智能体划分为同质类别，且异质性在极限下平均化。
• 正则化雅可比算法可实现有限群体中纳什均衡的精确分布式计算。
• 仿真结果验证了理论发现，确认了收敛性与计算可行性。