A bilevel NLP sensitivity‐based decomposition for dynamic optimization with moving finite elements
A bilevel NLP sensitivity‐based decomposition for dynamic optimization with moving finite elements
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DOI：
10.1002/aic.14339
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发表时间：
2014-03
期刊：
影响因子：
3.7
通讯作者：
Weifeng Chen;Zhijiang Shao;L. Biegler
中科院分区：
文献类型：
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作者：
Weifeng Chen;Zhijiang Shao;L. Biegler
最优控制在化学工程中有着广泛的应用，而最优控制的精确确定对于分离和反应过程的操作，以及间歇过程的操作策略和配方生成是必不可少的。在这里，一个同时配置的基础上移动有限元制定的解决方案的一类最优控制问题。该算法的新功能包括断点的控制配置文件和终止标准的基础上一个恒定的哈密顿配置文件的直接位置。该算法是稳定的，性能显着提高，通过分解的整体非线性规划（NLP）制定成一个内部问题，解决了一个固定的元素同时配置问题，和一个外部问题，调整有限元的基础上几个错误的标准。这两个问题的NLP求解器（内点优化器）以及NLP灵敏度组件，它提供了从内部问题到外部问题的衍生信息，这两个两级配方的帮助。这种方法证明了11个动态优化问题，从最优控制和化学工程文献。© 2014美国化学工程师学会AIChE J，60：966-979，2014
Optimal control has guided numerous applications in chemical engineering, and exact determination of optimal profiles is essential for operation of separation and reactive processes, and operating strategies and recipe generation for batch processes. Here, a simultaneous collocation formulation based on moving finite elements is developed for the solution of a class of optimal control problems. Novel features of the algorithm include the direct location of breakpoints for control profiles and a termination criterion based on a constant Hamiltonian profile. The algorithm is stabilized and performance is significantly improved by decomposing the overall nonlinear programming (NLP) formulation into an inner problem, which solves a fixed element simultaneous collocation problem, and an outer problem, which adjusts the finite elements based on several error criteria. This bilevel formulation is aided by a NLP solver (the interior point optimizer) for both problems as well as an NLP sensitivity component, which provides derivative information from the inner problem to the outer problem. This approach is demonstrated on 11 dynamic optimization problems drawn from the optimal control and chemical engineering literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 966–979, 2014