Abstract We present a sensitivity-based nonlinear model predictive control (NMPC) algorithm and demonstrate it on a case study with an economic cost function. In contrast to existing sensitivity-based approaches that make strong assumptions on the underlying optimization problem (e.g. the linear independence constraint qualification implying unique multiplier), our method is designed to handle problems satisfying a weaker constraint qualification, namely the Mangasarian-Fromovitz constraint qualification (MFCQ). Our nonlinear programming (NLP) sensitivity update consists of three steps. The first step is a corrector step in which a system of linear equations is solved. Then a predictor step is computed by a quadratic program (QP). Finally, a linear program (LP) is solved to select the multipliers that give the correct sensitivity information. A path-following scheme containing these steps is embedded in the advanced-step NMPC (asNMPC) framework. We demonstrate our method on a large-scale case example consisting of a reactor and distillation process. We show that LICQ does not hold and the path-following method is able to accurately approximate the ideal solutions generated by an NLP solver.

中文翻译：

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退化系统的基于灵敏度的快速经济模型预测控制

摘要 我们提出了一种基于灵敏度的非线性模型预测控制 (NMPC) 算法，并在具有经济成本函数的案例研究中对其进行了演示。与现有的基于敏感性的方法对基础优化问题做出强假设（例如线性独立约束条件暗示唯一乘数）相比，我们的方法旨在处理满足较弱约束条件的问题，即 Mangasarian-Fromovitz 约束条件（ MFCQ）。我们的非线性规划 (NLP) 灵敏度更新包括三个步骤。第一步是求解线性方程组的校正步骤。然后通过二次程序 (QP) 计算预测器步骤。最后，求解线性规划 (LP) 以选择提供正确灵敏度信息的乘数。包含这些步骤的路径跟踪方案嵌入在高级步骤 NMPC (asNMPC) 框架中。我们在一个由反应器和蒸馏过程组成的大型案例中展示了我们的方法。我们表明 LICQ 不成立，路径跟踪方法能够准确地逼近 NLP 求解器生成的理想解。