Optimal control of higher-order Hilfer fractional non-instantaneous impulsive stochastic integro-differential systems

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Journal of Engineering Mathematics Pub Date : 2024-04-17 DOI:10.1007/s10665-024-10358-y

T. Sathiyaraj, P. Balasubramaniam, Hao Chen, Seng Huat Ong

引用次数: 0

Abstract

Nowadays, engineers and biochemical industries have benefited greatly from optimal control analysis and its computational methods. Furthermore, the optimal control theory is a powerful instrument in infectious disease modeling and control of vibration in civil engineering structures under random loadings. In this paper, a new solution representation and optimal control of second-order Hilfer fractional stochastic integro-differential systems (HFSIDSs) with non-instantaneous impulsive (NI) are studied. Existence and uniqueness of solutions are proved in the finite-dimensional space by using Schaefer’s type fixed-point theorem with low conservative conditions on nonlinear part. Further, Lagrange problem is considered to establish optimal control results for HFSIDSs with NI. Finally, a pharmacotherapy type Hilfer fractional model is discussed in the example section.

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高阶 Hilfer 分式非瞬时脉冲随机积分微分系统的优化控制

如今，工程师和生物化学工业已从最优控制分析及其计算方法中受益匪浅。此外，最优控制理论也是传染病建模和土木工程结构随机载荷下振动控制的有力工具。本文研究了具有非瞬时脉冲（NI）的二阶 Hilfer 分数随机积分微分系统（HFSIDS）的新解表示和最优控制。利用 Schaefer 型定点定理和非线性部分的低保守条件，证明了有限维空间中解的存在性和唯一性。此外，还考虑了拉格朗日问题，以建立具有 NI 的 HFSIDS 的最优控制结果。最后，在示例部分讨论了药物治疗类型的 Hilfer 分数模型。

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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