用博弈论+强化学习提升微电网抗网络攻击能力
Game-Theoretic Resilience Framework for Cyber-Physical Microgrids using Multi-Agent Reinforcement Learning
- 构建攻防博弈框架，融合多种韧性指标形成统一收益矩阵
- 自适应防御使韧性提升18.7%，显著优于静态策略
- 适合电力系统安全、智能电网与强化学习交叉研究者
现代电力系统对信息物理基础设施的依赖加剧了定向网络攻击风险，亟需鲁棒且自适应的韧性策略。本文提出一个数学严谨的博弈论框架，结合量化韧性指标——供电比LSR、关键负荷韧性CLR、拓扑存活率TSS和分布式能源韧性评分DRS，通过层次分析法AHP整合为统一收益矩阵，评估攻防互动。框架被形式化为有限时域马尔可夫决策过程MDP，具备收敛性保证与计算复杂度边界。通过三个案例验证：1）静态攻击下的纳什均衡分析；2）高影响攻击场景；3）基于斯塔克尔伯格博弈、后悔匹配、Softmax启发式及多智能体Q学习的自适应攻击。理论分析提供收敛速率证明、PAC学习样本复杂度界与计算复杂度分析。在改进的IEEE 33节点配电系统上测试，集成分布式能源与控制开关，结果显示自适应防御相较静态方法在韧性上提升18.7%与2.1%，具有统计显著性。
原文摘要 · Abstract (English)
The increasing reliance on cyber physical infrastructure in modern power systems has amplified the risk of targeted cyber attacks, necessitating robust and adaptive resilience strategies. This paper presents a mathematically rigorous game theoretic framework to evaluate and enhance microgrid resilience using a combination of quantitative resilience metrics Load Served Ratio LSR, Critical Load Resilience CLR, Topological Survivability Score TSS, and DER Resilience Score DRS. These are integrated into a unified payoff matrix using the Analytic Hierarchy Process AHP to assess attack defense interactions. The framework is formalized as a finite horizon Markov Decision Process MDP with formal convergence guarantees and computational complexity bounds. Three case studies are developed 1. static attacks analyzed via Nash equilibrium, 2. severe attacks incorporating high impact strategies, and 3. adaptive attacks using Stackelberg games, regret matching, softmax heuristics, and Multi Agent Q Learning. Rigorous theoretical analysis provides convergence proofs with explicit rates , PAC learning sample complexity bounds, and computational complexity analysis. The framework is tested on an enhanced IEEE 33bus distribution system with DERs and control switches, demonstrating the effectiveness of adaptive and strategic defenses in improving cyber physical resilience with statistically significant improvements of 18.7% 2.1% over static approaches.
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