文章基本信息

标题：Parametric Stability Score and Its Application in Optimal Control
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作者：Ivan Mykhailiuk ; Kai Schäfer ; Christof Büskens 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2022
卷号：55
期号：16
页码：172-177
DOI：10.1016/j.ifacol.2022.09.019
语种：English
出版社：Elsevier
摘要：AbstractOptimization problems in the context of real-world applications often suffer from having multiple local solutions. When parameters within such a problem change, the corresponding solutions might differ significantly. However, it can be of interest for a practitioner to remain close to a nominal solution. In this work, we propose a novel concept to evaluate and compare the quality of local solutions with respect to parameter perturbations. We introduce the parametric stability score, which represents the largest possible perturbation magnitude such that the solution of a perturbed problem remains within user-defined bounds. It is defined as a global solution of a nonlinear bilevel program. In addition to a formal definition, we provide an efficient way to approximate the score numerically based on parametric sensitivity analysis. As an application scenario, we consider the optimal control of a pendulum on a cart. The model equations feature physical parameters that undergo perturbations. We obtain two different local solutions of the optimal control problem and calculate their stability scores. Our results indicate that a solution with a better cost does not necessarily have a better stability score. Finally, we validate the results by showing numerically that our approximations predict the actual stability score sufficiently well.
关键词：Keywordsnonlinear optimizationlocal solutionparametric sensitivity analysisbilevel optimizationoptimal control