Model Predictive Control (MPC) in building energy management requires transient thermal models balancing thermodynamic accuracy with computational efficiency. Standard spatial discretization triggers state-space inflation, paralyzing real-time solvers, while analytical Transfer Matrix Methods (TMM) suffer from high-frequency numerical overflow and assume material homogeneity. This paper introduces a frequency-domain framework based on the continuous spatial Riccati equation. A recursive admittance mapping strictly bounds exponential growth, preventing numerical instability. Regular perturbation theory analytically resolves continuous spatial property gradients ($λ$(x)) and non-linear T 4 radiative boundaries as equivalent harmonic source terms. This meshless approach eliminates spatial truncation errors. It analytically corrects peak heating load deviations of 21.9% in wetted media and mitigates artificial nocturnal cooling fluxes of 12.0 W/m 2 . Preserving an O(N ) spatial complexity, the framework structurally avoids state-space inflation, ensuring the high-speed execution demanded by multi-week MPC optimization.

翻译：建筑能源管理中的模型预测控制（MPC）要求瞬态热模型在热力学精度与计算效率之间取得平衡。标准空间离散化方法会导致状态空间维度膨胀，使实时求解器失效；而解析传递矩阵方法（TMM）存在高频数值溢出问题，且假设材料均匀性。本文提出一种基于连续空间Riccati方程的频域框架。递归导纳映射严格约束指数增长，防止数值失稳。正则微扰理论将连续空间物性梯度（$λ$(x)）及非线性T⁴辐射边界解析等效为谐波源项。该无网格方法消除了空间截断误差，可解析修正湿介质中21.9%的峰值热负荷偏差，并抑制12.0 W/m²的人为夜间冷却通量。在保持O(N)空间复杂度的情况下，该框架从结构上避免了状态空间膨胀，确保多周MPC优化所需的高速执行性能。