论文标题
主动子空间中的NMPC：降低递归可行性的降低性保证
NMPC in Active Subspaces: Dimensionality Reduction with Recursive Feasibility Guarantees
论文作者
论文摘要
降低决策变量是减少线性和非线性模型预测控制（NMPC）中计算负担的实用和经典方法。可用的结果范围从早期封锁想法到单数价值分解。对于更复杂的方案而言，似乎并不简单地保证退化摩尼子优化的递归可行性。将与输入有关的决策变量的空间分解为主动和不活动的补充，本文提出了一个通用框架，以有效地具有可行性的维度降低NMPC。我们展示了如何 - 独立于子空间的实际选择 - 可以建立递归可行性。此外，我们建议使用全球灵敏度分析以基于用户定义的标准以数据驱动方式构建主动空间。数值示例说明了提出的方案的功效。具体而言，对于化学反应堆，我们以$ 20-40 $的价格大幅减少了$ 20-40 $，闭环性能衰减小于$ 0.05 \％$。
Dimensionality reduction of decision variables is a practical and classic method to reduce the computational burden in linear and Nonlinear Model Predictive Control (NMPC). Available results range from early move-blocking ideas to singular-value decomposition. For schemes more complex than move-blocking it is seemingly not straightforward to guarantee recursive feasibility of the receding-horizon optimization. Decomposing the space of decision variables related to the inputs into active and inactive complements, this paper proposes a general framework for effective feasibility-preserving dimensionality reduction in NMPC. We show how -- independently of the actual choice of the subspaces -- recursive feasibility can be established. Moreover, we propose the use of global sensitivity analysis to construct the active subspace in data-driven fashion based on user-defined criteria. Numerical examples illustrate the efficacy of the proposed scheme. Specifically, for a chemical reactor we obtain a significant reduction by factor $20-40$ at a closed-loop performance decay of less than $0.05\%$.
