文章基本信息

标题：Some Necessary and Sufficient Conditions for Correctness of Linear Machine in Presence of Numerical Errors
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作者：Aditi Sharma ; Mani Bhushan
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2020
卷号：53
期号：2
页码：11368-11373
DOI：10.1016/j.ifacol.2020.12.547
语种：English
出版社：Elsevier
摘要：AbstractLinear machine (LM) has been recently proposed (Airan et al., 2017) for solving the point location problem which arises in explicit model predictive control (e-MPC). LM associates a linear discriminant function with each critical region identified in the offline phase in e-MPC. The solution to the online point location problem in the LM approach then simply corresponds to the region whose discriminant function attains the largest value amongst all the discriminant functions. LM involves two steps: (i) identification of neighbouring critical regions, and (ii) finding the discriminant functions by writing constraints involving discriminant functions of neighbouring pairs of regions. Both these steps involve solving linear programming (LP) problems. Similar to any other optimization problem, the constraints of the LP are satisfied with some tolerances. Even though theoretically sound, the resulting LM may not accurately identify the critical region due to the numerical errors arising from these tolerances. In the current work, we identify some conditions which can be used as an aid by the user to judge the accuracy of LM results. In particular, we give a necessary condition for step (i) whose violation will yield incorrect misclassification for some point location problems. We also propose a sufficient condition whose satisfaction guarantees the accuracy of linear machine solution despite numerical errors which may have crept in during step (ii) of the LM design. This condition needs to be evaluated for each specified point during the point location phase. We illustrate these ideas on the well known quadruple tank system.
关键词：Keywordspoint locationexplicit model predictive controlmulti-parametric programming