发表机构
Texas A&M Energy Institute; Artie McFerrin Department of Chemical Engineering, Texas A&M University（德州农工大学能源研究所; 德州农工大学阿蒂·麦费林化学工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究连续时间多参数最优控制中临界区域边界的形状判定，提出基于时变有效约束序列的五条规则，可预先区分超平面与弯曲边界，并在Newell-Lee蒸发器上验证了分类效果。
AI 中文摘要
连续时间中的多参数最优控制将初始状态空间划分为临界区域，每个区域都有其自身的控制律，涉及一组时变有效约束。两个相邻区域之间的边界要么是超平面，由一条线性方程以闭式形式给出，要么是必须计算的弯曲边界。时变有效约束的序列在定义临界区域边界的线性或非线性形状方面起着关键作用。在本文中，我们展示了如何在任何计算之前确定该形状。特别地，我们证明在两个条件下边界是超平面。第一，新约束在边界上的每个点处同时变为有效。第二，其他约束保持有效的持续时间在边界上的每个点处相同。否则，边界是弯曲的。这两个条件都可以从两个相邻区域的有效约束序列中读取，这给出了五条规则，每条规则产生一个超平面或弯曲边界。我们在Newell-Lee蒸发器上说明了这些规则，其中它们将七区域划分的八个边界分类为四个闭式给出的超平面和四个精确计算的弯曲边界。
英文摘要
Multiparametric optimal control in continuous time partitions the space of initial states into critical regions, each with its own control law involving a set of time-varying active constraints. The boundaries between two neighbouring regions are either hyperplanes, which are given in closed form by one linear equation, or curved boundaries, which must be computed. The sequence of time-varying active constraints plays a key role in defining the linear or nonlinear shape of a critical-region boundary. In this paper we show how to determine that shape prior to any computation. In particular, we show that the boundary is a hyperplane under two conditions. First, the new constraint becomes active at the same instant at every point of the boundary. Second, the durations for which the other constraints stay active are the same at every point of the boundary. Otherwise, the boundary is curved. Both conditions can be read from the sequences of active constraints of the two neighbouring regions, which gives five rules, each yielding a hyperplane or a curved boundary. We illustrate the rules on the Newell-Lee evaporator, where they classify the eight boundaries of a seven-region partition into four hyperplanes, given in closed form, and four curved boundaries, computed exactly.
