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A Solution to Fuller’s Problem Using Constructions of Pontryagin’s Maximum Principle
Moscow University Computational Mathematics and Cybernetics Pub Date : 2018-11-26 , DOI: 10.3103/s0278641918040039
Yu. N. Kiselev , M. V. Orlov , S. M. Orlov

The classical two-dimensional Fuller problem is considered. The boundary value problem of Pontryagin’s maximum principle is considered. Based on the central symmetry of solutions to the boundary value problem, the Pontryagin maximum principle as a necessary condition of optimality, and the hypothesis of the form of the switching line, a solution to the boundary value problem is constructed and its optimality is substantiated. Invariant group analysis is in this case not used. The results are of considerable methodological interest.

中文翻译:

使用庞特里亚金最大原理的构造来解决富勒问题

考虑经典的二维富勒问题。考虑庞特里亚金最大原理的边值问题。基于边值问题解的中心对称性,庞特里亚金最大值原理作为最优性的必要条件,并基于开关线路形式的假设,构造了边值问题的解,并证明了其最优性。在这种情况下,不使用不变组分析。结果具有相当大的方法学意义。
更新日期:2018-11-26
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