发表机构
Zhejiang University; Alibaba Group（浙江大学; 阿里巴巴集团）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对工业控制系统中高级持续性威胁与移动目标防御的随机博弈，提出动态低秩均衡计算方法，利用攻击-防御矩阵的低秩结构，实现高效、鲁棒的纳什均衡计算，并在电力系统测试中达到94%参数压缩和极小效用损失。
AI 中文摘要
针对工业控制系统（ICS）中高级持续性威胁（APT）的移动目标防御（MTD）已有成熟的博弈论公式化，但其实际价值取决于均衡计算：在工业状态维度下，全秩值迭代代价高昂，且由此产生的防御策略对对抗性扰动缺乏可认证的鲁棒性。我们首先揭示ICS动力学的攻击和防御影响矩阵本质上是低秩的：APT通过少数入口点渗透，而MTD每周期仅重新配置有限子集的组件。我们证明这种结构通过零和随机博弈的非光滑贝尔曼算子传播：一个连接物理和算法低秩的增广梯度矩阵证明每个贝尔曼目标都位于低维子空间附近，并给出最优值函数的显式误差界。由于这些子空间在值迭代下漂移，静态低秩投影不足。因此，我们提出动态低秩均衡计算（DLR-NE），它在每次迭代中增广秩为r的搜索空间，正则化核心矩阵谱，并通过截断SVD进行回缩，每一步提取纳什均衡。随之而来有四个保证：显式逼近误差；几何收敛到具有五个物理解释误差源的邻域；每步成本O(nr^2)，比全秩值迭代加速Theta(n/r^2)倍；以及鲁棒性，其中单一权重权衡精度与可认证安全性。在非线性电力系统测试平台上的实验证实了每个预测，在0.16%效用损失下实现了94%的参数压缩。
英文摘要
Moving target defense (MTD) against advanced persistent threats (APTs) in industrial control systems (ICS) has well-established game-theoretic formulations, but their practical value hinges on equilibrium computation, which faces two gaps: full-rank value iteration is prohibitively expensive at industrial scale, and the resulting defense strategies admit no certified robustness against adversarial perturbations. We first reveal that the attack and defense influence matrices of ICS dynamics are intrinsically low-rank: APTs infiltrate through a handful of entry points and MTD reconfigures only a few components per cycle. Our theory makes four contributions. First, an augmented gradient matrix certifies that the low-rank structure propagates through the non-smooth Bellman operator of the zero-sum stochastic game, so that every Bellman target lies near a low-dimensional subspace and low-rank truncation incurs an explicit error bound (Lemma 1, Theorem 1). Second, we propose the Dynamical Low-Rank Nash Equilibrium algorithm, named DLR-NE, which augments the rank-r search space each iteration, regularizes the core matrix spectrum, and retracts via truncated SVD, and prove that it converges geometrically to a neighborhood whose error decomposes into five physically interpretable sources (Theorem 2). Third, its per-step cost is O(nr^2), a Theta(n/r^2) speedup over full-rank value iteration (Theorem 3). Fourth, a single weight trades accuracy against a certified sensitivity bound of the induced defense strategy under core-matrix perturbations (Corollary 1). Six experiments on a nonlinear power-system testbed confirm each prediction, with 94% parameter compression at 2.3% utility loss. All experimental data and code are publicly available.
CommentsRegular Paper, under review at Automatica (submission 26-2265). v2: corrected the utility-loss figure in Experiment 5 (2.3%). This preprint is the full-length version; the journal submission is a condensed 16-page two-column version. Source code: https://github.com/tz98lab/dlr-ne-ics-security
