Solving convex uncertain PDE-constrained multi-dimensional fractional control problems via a new approach

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Engineering Mathematics Pub Date : 2024-03-16 DOI:10.1007/s10665-024-10338-2

Anurag Jayswal, Ayushi Baranwal, Tadeusz Antczak

引用次数: 0

Abstract

In this paper, the class of uncertain multi-dimensional fractional control problems with the first-order PDE constraints is investigated. The robust approach and the parametric method are applied for solving such control problems. Then, robust optimality is analyzed for the considered PDE-constrained multi-dimensional fractional control problem with uncertainty. Further, the exact absolute penalty function method is used for solving control problems created in both the aforementioned approaches. Then, under appropriate convexity hypotheses, exactness of the penalization of this exact penalty function method is investigated in the case when it is used for solving the considered control problem with uncertainty. Further, an algorithm based on the used method is presented, the main goal of which is to illustrate the precise steps to solve the unconstrained multi-dimensional non-fractional control problem with uncertainty associated with the constrained fractional control problem.

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用新方法解决凸不确定 PDE 受限多维分数控制问题

本文研究了一类具有一阶 PDE 约束的不确定多维分数控制问题。在求解这类控制问题时，采用了鲁棒方法和参数法。然后，分析了所考虑的具有不确定性的 PDE 约束多维分数控制问题的鲁棒最优性。此外，在解决上述两种方法所产生的控制问题时，采用了精确绝对惩罚函数法。然后，在适当的凸性假设下，研究了这种精确惩罚函数方法在用于解决所考虑的具有不确定性的控制问题时的惩罚精确性。此外，还介绍了基于所使用方法的算法，其主要目的是说明解决与受约束分数控制问题相关的不确定性无约束多维非分数控制问题的精确步骤。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Engineering Mathematics 工程技术-工程：综合

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

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