用归一化流建模化学过程随机动态，提升控制稳定性与准确性。
Least Squares and Marginal Log-Likelihood Model Predictive Control using Normalizing Flows
- 用条件归一化流显式学习状态概率分布，捕捉非平稳随机特性。
- 相比基准控制器，闭环开环误差减半，约束违规次数更少。
- 边际对数似然目标在小样本下表现更稳定，适合资源受限场景。
现实中的（生物）化学过程常呈现具有复杂相关性和依赖状态的随机动态。模型预测控制（MPC）需考虑此类波动以保证可靠性能。然而，多数过程模型仅在确定性预测上添加平稳噪声。本文提出使用条件归一化流作为离散时间模型来学习随机动态。归一化流能显式学习给定前序状态和控制输入下的状态概率密度函数（PDF）。除标准最小二乘（LSQ）目标外，本文还基于显式PDF与马尔可夫链模拟推导出边际对数似然（MLL）目标。在反应器案例研究中，归一化流MPC使开环与闭环情况下的设定点误差降低至基准控制器的一半；同时，机会约束导致的约束违规次数也更少。MLL目标在小场景集下表现出略优的稳定性。
原文摘要 · Abstract (English)
Real-world (bio)chemical processes often exhibit stochastic dynamics with non-trivial correlations and state-dependent fluctuations. Model predictive control (MPC) often must consider these fluctuations to achieve reliable performance. However, most process models simply add stationary noise terms to a deterministic prediction. This work proposes using conditional normalizing flows as discrete-time models to learn stochastic dynamics. Normalizing flows learn the probability density function (PDF) of the states explicitly, given prior states and control inputs. In addition to standard least squares (LSQ) objectives, this work derives a marginal log-likelihood (MLL) objective based on the explicit PDF and Markov chain simulations. In a reactor study, the normalizing flow MPC reduces the setpoint error in open and closed-loop cases to half that of a nominal controller. Furthermore, the chance constraints lead to fewer constraint violations than the nominal controller. The MLL objective yields slightly more stable results than the LSQ, particularly for small scenario sets.
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