Abstract Necessary conditions of optimality (NCO) tracking is a promising approach to run-to-run optimization of batch processes, by converting the optimization problem into a feedback control problem. Since batch processes often contain numerous decision variables that hamper input adaptation in a feedback control manner, the directional effect of uncertainty has been utilized to reduce adaptation directions. This paper proposes an active approach that can further simplify the design of NCO tracking controllers for run-ro-run optimization of batch processes. The idea is to actively restrict the plant inputs in an optimal subspace, prior to the separation of constraint- and sensitivity-seeking directions of plant inputs. For this purpose, an extended system is constructed and then the system is operated by the so-called surrogate variables. Depending on the dimensions of active constraints and uncertain parameters, two cases are distinguished and their NCO tracking controllers are designed respectively. In addition, when the number of parameters is greater than the constraints, the neighboring-extremal based output feedback is incorporated into the active approach, such that the time-consuming gradient evaluations are avoided hence convergence is accelerated. In both cases, the number of adapted directions equals to the number of uncertain parameters. A numerical example and a batch distillation column are investigated to show the new methodology.

中文翻译：

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一种减少空间的 NCO 跟踪和输出反馈优化控制具有参数不确定性的批处理的主动方法

摘要 通过将优化问题转化为反馈控制问题，优化必要条件 (NCO) 跟踪是批处理优化的一种有前途的方法。由于批处理通常包含许多以反馈控制方式阻碍输入适应的决策变量，因此已利用不确定性的方向效应来减少适应方向。本文提出了一种主动方法，可以进一步简化 NCO 跟踪控制器的设计，用于批处理的 run-ro-run 优化。这个想法是在分离植物输入的约束和敏感性寻求方向之前，将植物输入主动限制在最佳子空间中。为此，构建了一个扩展系统，然后通过所谓的替代变量来操作该系统。根据主动约束和不确定参数的维度，区分两种情况，分别设计它们的NCO跟踪控制器。此外，当参数的数量大于约束时，基于相邻极值的输出反馈被纳入主动方法，从而避免耗时的梯度评估，从而加速收敛。在这两种情况下，适应方向的数量等于不确定参数的数量。研究了一个数值例子和一个间歇蒸馏塔来展示新的方法。将基于相邻极值的输出反馈结合到主动方法中，从而避免了耗时的梯度评估，从而加速了收敛。在这两种情况下，适应方向的数量等于不确定参数的数量。研究了一个数值例子和一个间歇蒸馏塔来展示新的方法。基于相邻极值的输出反馈被合并到主动方法中，从而避免了耗时的梯度评估，从而加速了收敛。在这两种情况下，适应方向的数量等于不确定参数的数量。研究了一个数值例子和一个间歇蒸馏塔来展示新的方法。