我的随机网络控制器允许次优到什么程度？面向托管AI数据中心的电网的完成证书
How suboptimal is my stochastic network controller allowed to be? Completion certificates with application to power grids hosting AI data centers
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中文总结 AI 辅助
本文提出一种基于HJB子解和路径积分控制的证书方法，量化电网控制器在托管AI数据中心时的次优性，并在IEEE 118节点系统上验证了其有效性。
中文摘要 AI 辅助
电网开始容纳AI数据中心，其需求可能突然且相关地变化，运营商和规划者必须决定现有控制器能否吸收由此产生的瞬态，以及在哪里值得安装新的灵活性。我们将此问题表述为随机控制中的一个问题：一个可实现的控制器离最优有多远？对于具有仿射、状态无关驱动、加性且可能退化的噪声以及二次控制成本的受控扩散，任何Hamilton-Jacobi-Bellman (HJB) 子解都从下方界定最优成本，而模拟从上方界定部署成本，因此它们的差距证明了允许的次优性。我们通过路径积分控制构造子解，通过完成控制几何：将控制Gramian扩大直到与物理噪声匹配，使问题线性可解，其Feynman-Kac值是一个自动下界，其HJB残差恰好是虚构控制的能量。对偶噪声缩减构造可以更紧，但需要曲率条件。该几何产生了规划规则：按局部噪声方差的比例定价控制权，并使用影子值指导稀疏增强。对于IEEE 118节点系统在严重负荷损失后的非线性随机摆动动力学，一个简单的发电机控制器在均匀强迫下被证明在最优的2.8%以内；在非均匀强迫下，均匀价格下的差距为39%，而在重新定价相同总权后差距为1.2%，无需添加任何硬件。
英文摘要
Power grids are beginning to host AI data centers whose demand can change abruptly and in a correlated way, and operators and planners must decide whether existing controllers can absorb the resulting transients and where new flexibility is worth installing. We cast this as a question in stochastic control: how far from optimal is an implementable controller? For controlled diffusions with affine, state-independent actuation, additive and possibly degenerate noise and quadratic control cost, any Hamilton-Jacobi-Bellman (HJB) subsolution bounds the optimal cost from below and simulation bounds the deployed cost from above, so their gap certifies the permissible suboptimality. We construct subsolutions from path-integral control by completing the control geometry: enlarging the control Gramian until it matches the physical noise makes the problem linearly solvable, and its Feynman-Kac value is an automatic lower bound whose HJB residual is exactly the energy of the fictitious control. A dual noise-deflation construction can be tighter but requires a curvature condition. The geometry yields planning rules: price control authority in proportion to local noise variance, and use shadow values to guide sparse reinforcement. For nonlinear stochastic swing dynamics of the IEEE 118-bus system after a severe load loss, a simple generator controller is certified within 2.8% of optimal under homogeneous forcing; under heterogeneous forcing the gap is 39% with uniform prices and 1.2% once the same total authority is repriced, before any hardware is added.
发表机构
- University of Arizona（亚利桑那大学）
机构由 AI 辅助整理，请以论文原文为准。
